The Rossoneri coach expected the difficulties considering his inexperienced squad and revealed that Mario Balotelli could return during the Guinness ICC.
The Rossoneri fell five goals behind inside the opening 36 minutes thanks to a double from Edin Dzeko, after earlier strikes from David Silva, Richard Wright and Aleksandar Kolarov.
Stephan El Shaarawy, who struck twice, and Andrea Petagna restored some pride for Allegri's men, but the Rossoneri manager insists he while he did expect his side to struggle, he was still bitterly disappointed with the lack of application during the early exchanges.
"We did badly in the first half-hour, as there was some timidity and we didn’t put in a single tackle," Allegri told Sportmediaset. "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 and the Guinness International Champions Cup, 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," Allegri said. "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 Sao Paulo in the consolation match of the Audi Cup on Thursday before departing for the USA.