The Rossoneri ranout 3-1 winners as Zlatan Ibrahimovic saw red on the day.
D'Aversa rapped: “We didn't do enough when against 10 men. We had also compromised the game in the first half, as we were too timid and hesitant against a great team, but one that had just dropped points with Sampdoria. That showed they struggle when put under pressure and we just weren't aggressive enough.
“The red card gave us a way back in, but we did the damage in the first half. I replaced Gervinho at the break, but there were many players who were below par and had a slow tempo in the first half.
“We came out with a different attitude after the break, but we could've done better. We conceded those two goals far too easily and a team trying to save itself from the drop cannot afford to give away goals so cheaply.
“It was a lack of determination and character, that's what was unacceptable. We were too timid, didn't run off the ball, didn't provide options.
“The second half was better, but not just because we were against 10 men, as the attitude was different from the first minute of the half.
“Milan gave us a 'gift' as it were with the red card, but I didn't have attacking options to take off the bench and shake things up."