Goals from Robinho, Antonio Cassano and Antonio Nocerino gave the Milan side a convincing win, and Allegri praised his squad's performance.
"Everyone played a good game," said the coach according to reports by La Gazzetta dello Sport.
"We already set our stall in the first few minutes and tried to break through the middle, but then the quality of our individuals shone through and made the difference."
"Tonight was an important game, all my players understood that the five points [we had accumulated] in the standings were too few and so had to start winning," he continued. "Maybe against Juve we were tired but we also played poorly on a technical level."
The 44-year-old believes this win will catapult AC Milan back Serie A.
"Forgetting about the results of our rivals, it was important to get back to winning convincingly and now we must catch up as many points as possible to cancel out the difference between us and the sides at the top," said Allegri.
"The three points will allow us to climb the rankings, but only slowly as the season is long. We must continue like this", he concluded.