Odegaard on point
There are a host of negatives to get through in this game so let's quickly focus on one of the undoubted positives that arose from it.
It's coming up to one year since Martin Odegaard signed for Arsenal - the first time around at least - and with each passing day it's looking like a tremendous piece of business.
The Norwegian had his doubters due to his lack of numbers in terms of goals and assists, with many preferring a permanent acquisition of James Maddison in the summer, but those who focus on that miss what else he brings to the team.
On Sunday, Odegaard was excellent at picking up pockets of spaces in between the tightly compressed Burnley 4-4-2 and progressing the Gunners up the pitch.
In the first half he created more chances than anyone else on the pitch and managed more shots on target than any of his teammates, and continued that form into the second where he was desperately unlucky to see a free-kick go just over the bar and graze the roof of the net.
With regular game time at a stable home for the first time in his club career, the 23-year-old looks to be growing in stature with each passing game and is happy to boss his teammates around.
There were several instances where he could be seen barking instructions to the likes of Bukayo Saka and Gabriel Martinelli, while also guiding Albert Sambi Lokonga through difficult periods in the game.
After what happened against Liverpool it would seem that Kieran Tierney is next in line to be captain at the Emirates when a permanent decision is made.
But with performances like this and the respect of his teammates, surely Odegaard cannot be far behind when it comes to candidates for the role.
Transfer decisions questioned
For the second game in a row as Arsenal were up against it looking for a result, Mikel Arteta was forced to turn to his bench and see very little staring back at him.
Ryan Alebiosu, Salah-Eddine, Charlie Patino, Omari Hutchinson and Mika Biereth are all supremely talented youngsters who have impressed in Kevin Betsy's under-23 side this season, but they have a total of zero Premier League minutes between them. To expect them to change the game would have been too much.
This left Eddie Nketiah as the only real card Arteta had to play, but after replacing Emile Smith Rowe, the 22-year-old was again largely ineffective, even if he was slightly better than in his anonymous cameo against Liverpool on Thursday.
Perhaps Nuno Tavares could have been introduced as a more attack-minded right sided presence than Ben White, or the Portuguese could have replaced Rob Holding to allow for superior playing out from the back, but really that is clutching at straws. The reality is that when a push from the bench was needed, there was simply nothing there.
A degree of sympathy does have to be extended to Arteta in this instance.
Thomas Partey and Granit Xhaka should have been available, but both were recklessly sent off in previous games, while the likes of Nicolas Pepe and Mohamed Elneny were way at the Africa Cup of Nations. But those sentiments only go so far.
Much of these problems that Arsenal are going through do feel somewhat self-inflicted.
While the wheels were in motion a long time before Ainsley Maitland-Niles loan move to Roma, you can't help but think that he could have been useful across any of these fixtures in January in which the Gunners have failed to win a game.
Flo Balogun may have definitely been in need of a loan move too, but with Arsenal now goalless in four matches for the first time since 2005, you wonder if delaying his departure to Middlesbrough may have been wise.
Of course, both decisions can reasonably be defended, but if Arteta was going to take them, then surely incomings could have been planned to help make up for the loss in numbers.
The Spaniard was asked about this after the game and stated that he felt a degree of realism was required when analysing his side's transfer decisions this month.
"I think that's the dream of every manager, to have them in the team on the first day, but it isn't realistic," the 39-year-old said in his post-match press conference. "And in this window as well, the history of this window, a lot of them happen right at the end."
There may be some arrivals late in the window, but this seemingly avoidable winless month has the potential to be fatal to Arsenal's top four hopes. Come the end of the season, they will be hopeful that isn't the case.
Arsenal shown what they need to do to get top four
Let's start with something that might seem strange to read. Alexandre Lacazette didn't actually have that bad a performance on Sunday.
Unlike on Thursday against Liverpool where the Frenchman drifted in and out of the game, lacked centrality and could not link the play, he was a presence in attack off whom the likes of Emile Smith Rowe, Bukayo Saka, Martin Odegaard and Gabriel Martinelli could bounce, was a leading presence constantly in David Coote's ear about Burnley's persistent fouling and at times the 30-year-old even created his own opportunities by dribbling past Clarets defenders.
But when it comes to a striker's most important role in football, Lacazette was found painfully wanting.
The most gilt-edged missed chance was the open goal spurned after some fine work by Smith Rowe to dribble to the byline and lure Nick Pope away from his net in the second half.
There were plenty of others and as the Frenchman stood with his head in his hands at the full-time whistle, the biggest problem facing this Arsenal squad became painfully clear.
Perhaps we could analyse how the Gunners have gone from a position of having so many forwards that they were unable to sign the likes of Lautaro Martinez or Tammy Abraham in the summer, to now having so few dependable options in attack that Lacazette will play no matter how many chances he passes up Lacazette will play, but ultimately it doesn't change the Gunners predicament.
With just a week remaining of the transfer window there is one area above all else where they need to strengthen.
Pierre-Emerick Aubameyang does not appear to be coming back, Eddie Nketiah doesn't seem good enough, Flo Balogun is on loan and Gabriel Martinelli seems to be a full-time winger these days, so if Arsenal are to fix their centre-forward crisis, then they will have to do so in the transfer market.
When asked about the issue in his post-match press conference, Mikel Arteta indicated that he was willing to bring someone in, but only under certain circumstances.
"Players that come here have to be able to take us to the next level," the Spaniard said. "We already have a level, and we want to see much better standards than we already have, and that is how we're going to recruit."
Factoring in the long-term ambitions of the project Arsenal are trying to enact the at the Emirates is of course important in the signing of players this window, but at the same time you wonder if perhaps Arteta and Edu aren't sensing the opportunity that they have here.
Having had such an impressive run pre-Christmas the Gunners position has changed from being fine with top six, to one where if they are not in the top four by the end of the season then there will definitely be a sense of disappointment.
Sure, they can wait till the summer to strengthen, where deals will be much easier to do, but next season, the chances are, Manchester United will be much stronger, Tottenham will look to kick on under Antonio Conte, and previous Champions League contenders like Leicester will be back in the picture.
Assuming the top three are out of sight, this is probably the best chance Arsenal are going to have at getting top four for a long while, but with Lacazette and Nketiah as their striking options, you wouldn't bet on them getting it.
The games like the 0-0 draw against Burnley are ones where top level strikers give you three points instead of one.
If the Gunners want to go to the next level of the project in north London, then they would be wise to get such a player now instead of waiting until the summer when it might be too late.
Off to Dubai
This game may have left an underwhelming taste in Arsenal fans mouths, but it's one that they're going to have to get used to, as there is now not a game for almost three weeks.
It certainly seems like this break has come at the right time for the Gunners, who clearly need to give players a rest and recharge some batteries ahead of what will hopefully be a charge for the top four in the final stages of the season.
Takehrio Tomiyasu, for example, will finally be able to rest his calf injury that has been causing him trouble for over a month now, while Emile Smith Rowe will get to give his groin some much needed rehabilitation.
After the game Mikel Arteta revealed how he plans to spend the next few weeks with matches in such short supply.
"We're going to go away, we're going to have a training camp all together in a different environment," the Spaniard said. "Reunite, refocus and let's have a good go because there's still a lot to play for."
The camp will be in Dubai, and a bit of warm weather training is surely what's required for this group, who are starting to show signs of fatigue after what has been a gruelling past month fixture-wise.
On Sunday, at one point in the second half fitness coach Shad Forsythe had to sprint to the touchline to give Ben White an energy gel, while Kieran Tierney could barely run for the final five minutes of the match.
Of course Arteta, Edu, Richard Garlick and the rest of the Gunners recruitment team will have their focus on bringing players in during the break, and there will be a hope that they could even be registered in time to join the travelling group.
Only time will tell, but this time off could be a period we look back on in a similar manner to we how we now view the first international break of the season in retrospect.
Arsenal are exhausted and demoralised in a way they probably haven't been since that time in early September.
Arteta described that period as his best time in football. He'll be hoping to go one better this time around.
