The Rossoneri fell five goals behind inside the opening 36 minutes thanks to a double from Edin Dzeko, after earlier strikes from David Silva, Micah Richards and Aleksandar Kolarov.
Stephan El Shaarawy, who struck twice, and Andrea Petagna restored some pride for Allegri's men, but the Rossoneri trainer insists that while he did expect his side to struggle, he was still bitterly disappointed with their lack of application during the early exchanges.
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"Many of the players had never been in an atmosphere like this. At this moment, with the recent internationals and many out of action with injuries, we knew that we were going to run into some difficulties.
"We should’ve done better in terms of character, but then we got the game back on track and in the second half went close to making it 5-4. There are players who had a decent game today.
"We are a team with seven or eight players under 20, so we must not be affected by paranoia after such defeats. It was impossible in the circumstances to think of coming here and dominating Manchester City."
Ahead of the club's departure for a tour of USA, Allegri revealed that his squad will imminently be buoyed by the return of some key personnel.
"In the United States we’ll have Mario Balotelli, Riccardo Montolivo and Cristian Zapata back, while Matias Silvestre will also arrive," the San Siro boss added.
"Stephan El Shaarawy has only had four training sessions, plus Nigel de Jong and Sulley Muntari are improving their fitness levels."
Defeat against City means that Milan will face the loser of Bayern Munich-Sao Paulo on Thursday.