Milan opened their European campaign with a 2-0 win.
Allegri said: "We do have to improve, as we gave the ball away too much and tried to force the passes through, but it was a good reaction from the side to earn victory.
"The lads have heart and desire, as they know a game is always open until the final whistle, as we saw against Torino. What we do need to improve is how we read the game, knowing when to take up the tempo or slow it down. We started playing Celtic's game with long balls, which is what we should not be doing.
"We must always try to think positive. I have faith in the last 15-20 minutes of a game, as I know anything can happen there. The substitutions helped, as they did on Saturday.
"We won our first Scudetto thanks to our form from January onwards, while we lost the second title because of injuries. I often consider players on the bench to be more important than those in the starting XI."
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