Juventus were 1-0 winners at United in the Champions League on Tuesday thanks to a first-half goal from Paulo Dybala to record a third Group H triumph.
"It was a good team performance and we deserved the victory," Allegri said to Sky Sport Italia.
"We won a lot of balls in the air, Alex Sandro played it simple and did very well in defence. We controlled the tempo in the first half and had chances to score more goals, getting the final or penultimate pass wrong, but the build-up was largely correct.
"Naturally we can play without (Mario) Mandzukic, someone has to get into the box. It was important against Manchester United to keep the ball to ground and attack around Nemanja Matic.
"We still make too many mistakes on the final ball, as we had so many more chances and half-chances that we didn't develop properly. A couple of times it was the player with the ball, another couple it was the player who didn't peel away from his marker to reach the space."
78 - Rodrigo Bentancur completed the most passes (78) in the game between Manchester United & Juventus, with 91% passing accuracy. Director. pic.twitter.com/P2tuN6E6aZ— OptaJavier (@OptaJavier) October 23, 2018
Allegri demurred, though, when it was put to him that Juventus should be considered favourites to win the Champions League.
"There has been a constant growth process throughout the team and the club," Allegri added.
"Games must be read and there are times where you don't need to lunge forward.
"We didn't read it properly against Genoa, but this evening the team proved it can read the moments and strike at the right time."