The trainer felt his side's victory against the Elefanti served as proof that their late run of results were no flash in the pan, while he reflected on Pablo Barrientos' red card
Goals from Kevin-Prince Boateng and Stephan El Shaarawy handed the Rossoneri their first successive league victories of the season, despite Nicola Legrottaglie's header to open the scoring for the Sicilians.
"It was a tough match against Catania. They closed us down and took the lead from a corner, where we were a bit too passive," the Milan coach told reporters after the match.
"Catania did well in many aspects in the first half, and we only started playing well when I asked my players to dribble and pay greater attention to the dead ball because Catania are very good from these positions.
"The match was balanced, especially in the first half. In the second half, we improved and benefitted from numerical superiority.
"It's an important victory because it gives us continuity and makes our latest results count."
Allegri then claimed that wantaway Catania winger Pablo Barrientos' dismissal proved instrumental in both his side's fortunes and his tactical outlook on the match, as he also reserved praise for Boateng's performance.
"I wanted to play Montolivo in front of the defence in the second half, but then the red card changed everything," he added.
"Like against Juventus, Boateng had another good game with the right level of intensity. He is finding his feet in a role somewhat different to his usual position.
"Barrientos had to be less hasty in making the foul that led to his sending off. The red card seemed correct."
Milan temporarily move to seventh in the Serie A standings following their haul of three points at San Siro.