Juve fell to a humbling 4-1 defeat against Zinedine Zidane's side in Cardiff last May and are preparing to do battle for the first time since then in this term's quarter-finals.
Allegri was frustrated with his team's lack of concentration in that game, but believes the experience has made them a better side.
Speaking at his pre-match news conference, he said: "Of course, we have watched the final again several times, and I would say that the team, especially in Europe but also in Serie A, has improved a lot, especially in managing the difficult moments during the match.
"It was a very important lesson to grow and to improve, we had a good first half and then in the second half we should have managed the ball much better and we had to deal with it in a calmer way.
"That's something that influenced us. From a psychological view the team has certainly made huge strides since then.
"The important thing is to stay very focused and stay in the match without giving anything up."
While Madrid's LaLiga form has been inconsistent this season, Allegri has seen enough from their Champions League displays to know his side could be punished at any moment.
He added: "We have to be very intelligent in knowing how to manage the match, because as I've said before, they have such technique, precision and accuracy when they break.
"They're absolutely frightening when there's an open pitch, they can reach the box in two or three passes so we'll have to be really attentive and we'll have to use our defence as a foundation to attack.
"Our ambition is to play on the same level and be able to beat them."