Inter defender Marco Materazzi was sent off after he recieved a second yellow card, after celebrating his goal.
Mancini said: “Playing in 10 men with Zlatan Ibrahimovic carrying an injury and Patrick Vieira limping with a sore foot is not at all easy.
“I only had one substitution left and in this condition I had a few problems. On top of that, in the final 20 minutes I had nobody left to hold the ball up in attack, so we were under siege.
“If we hadn’t been left in 10 men, we would’ve scored more goals and not suffered any pressure at all. Red cards and injuries change the face of a game, but my men were fantastic to play like that in the last 20 minutes.”