The 45-year-old coach has admitted his side were far from impressive in the early stages of Sunday's victory, but took consolation from their second-half showing
Second-half goals from Bojan Krkic and Giampaolo Pazzini helped the Rossoneri to a comfortable 2-0 lead at San Siro, before Michele Paolucci pegged one back for the visitors in the closing stages of the encounter.
"We put in a very poor performance before the break and could have gone a goal down. We improved in the second half, though, and created a lot of chances. It's a shame that we conceded a goal late on," Allegri said at a press conference.
"We struggled with the pace of the game in the first half. That's why we changed our game-plan and that helped us back in the match. It was a good game in the end.
"It is always a bit difficult to get going again after the Christmas break."
Milan currently sit seventh in the Serie A table with 30 points from 19 games.