Former Celtic star Kris Commons reckons Ange Postecoglou will know he has to improve his rearguard ahead of next season.
The Premiership leaders are on the verge of title glory but were made to sweat by rivals Rangers during Sunday's 1-1 draw at Parkhead.
But that point keeps Postecoglou's men in charge as they close in on title glory in the Australian's first season in charge.
However, Commons believes the current defence suffers from a "glass jaw" when they step up in competition.
And big challenges likely lie ahead for Celtic with a spot in the Champions League group stage looming.
Speaking in the Daily Mail, he said: "I still feel like Celtic cough up far too many chances in big games against opposition who have some quality to exploit them in the final third.
"It's all well and good when you are dominating possession of the ball and scoring five or six goals against the likes of Dundee, St Mirren or St Johnstone.
"Against the smaller teams, Celtic press so high and so aggressively that they absolutely squeeze the life out of their opponents.
"There have been some games this season where they have enjoyed well over 80 per cent of possession. It's incredible to watch when they are in full flow.
"But there's still a nervousness and a fragility to their defence against teams with a bit more quality and bravery to engage them higher up the pitch.
"We've seen it all season. In conceding 15 times across six games in the group stage of the Europa League, Postecoglou's side shipped more goals than any other team in the competition.
"Bodo/Glimt then ran riot in the Europa Conference League, beating Celtic 5-1 on aggregate over the two legs.
"There's a glass jaw to this Celtic team and we saw it once again against Rangers yesterday. Plainly, Rangers will be kicking themselves that they didn't leave Parkhead with three points.
"Celtic were there for the taking.
"In the end, they were lucky to draw. Fashion Sakala could quite easily have had a hat-trick on a different day.
"Ryan Kent also missed a good chance, while Joe Hart produced a great save to deny Scott Arfield in the second half.
"Don't get me wrong, Celtic missed a few chances of their own. But if we're talking about how Postecoglou can improve this team, the defence looks to be an obvious starting point.
"There's no doubt Carl Starfelt has improved over the course of the season from the player who first arrived in Glasgow last summer.
"He can look good at times and, in fairness, he dealt with a lot of danger really well yesterday. But he still makes me nervous.
"He's one of these players who always just seems liable to throw in a mistake out of nowhere. Particularly in possession of the ball, he doesn't inspire confidence.
"Cameron Carter-Vickers has been good but, in the bigger picture, he was still part of a Celtic defence that coughed up far too many chances.
"You have to remember that this was a Rangers team who were playing without a recognised striker in the absence of both Alfredo Morelos and Kemar Roofe. Sakala is not a natural No 9.
"Yet Celtic still had trouble dealing with Rangers' attacking threat. That's an area Postecoglou must address moving forward."
