Allegri admitted that while he was glad to claim all three points, he was disappointed in the way his side conceded possession once they went ahead.
"The performance was one of great intensity and unfortunately we conceded a goal at the first chance," he told Sky Sport Italia.
"We could've scored more, but in any case were able to win with a two-goal cushion. The one thing I'd like to see is a better control of possession after taking the lead, but overall I liked the team. We are pushing forward and the work is starting to bear fruit."
Today's result was Milan's first win in six Serie A matches.