Inter looked like they were heading seven points clear at the top of the Serie A table with a game in hand when Ivan Perisic gave them a first half lead but Olivier Giroud’s quick fire double handed the initiative to Stefano Pioli’s men in the final 15 minutes.
Before the Giroud show, Inter should have been further ahead but for some brilliant saves by AC Milan goalkeeper Mike Maignan.
"This is football. We dominated in every way but weren't sharp at the end. They were lucky on the first goal and were smart on the second," Inzaghi said after the game.
"I saw a derby with one-way traffic for 60 minutes. In the final 25 minutes, we weren't as sharp or as in control, and the game was more open to individual incidents.
"We know it's a defeat that hurts, but strong teams must be able to analyse their errors.
"If we played it again 10 times, we might lose it once. We all know how important the derby is; we didn't deserve to lose, but that is football.
"Until the equaliser, we had allowed Milan practically nothing. It's a tough lesson, but a valuable one to make us more determined to kill off games so this doesn't happen again."
