The Spaniard took his fourth third-place finish in five races at the Miami Grand Prix, as he admitted that there is now a hunger to start delivering better results.
But rather than start setting unrealistic expectations for the battle ahead, Alonso said Aston Martin needed to accept that Red Bull remained a clear step ahead.
However, he believed that at some point a weekend would come when Red Bull got it wrong – and it was essential that Aston Martin was therefore in the position to make the most of it.
“Obviously, we want to step one step higher on the podium for P2 and eventually one day we have an opportunity to win a race,” he said after the Miami Grand Prix.
“But at the moment it didn’t happen because Red Bull is better than us. It’s stronger, it’s faster and the reliability has been always outstanding for them as well, finishing both cars in every race.
“But if one day there is a crack there, if there is an opportunity, we need to make sure we are in that position and we’re still not making mistakes at any point in the weekend.”
Although Alonso has been able to match the pace of Red Bull in some race stints, its rival still has a clear margin over the full grand prix distance.
That is why he thinks it is too early to believe that Aston Martin can find a step forward in pace to challenge the world champion squad just yet, but he suggests things could be different later in the campaign.
“I think the year is going to be difficult,” he said when asked about the prospects of a win. “The gap is quite big even though I think today has been our best race pace yet in the season.
“We finished, I think, closest to the leaders, with no safety cars, and nothing in the race and we’re still quite fast. So, let's see. I think the season is going to be long.
“Hopefully some of the tracks we will be a little bit closer to them, and some of the upgrades that we will bring later in the season maybe put us in a different or more competitive position.
“But I think our main focus, to be honest, is just looking behind and trying to keep Mercedes and Ferrari in the constructors’ championship under control. But I think Red Bull, we have to accept they are doing a better job than everyone else and we need to do a better job.”