Christian Pulisic had Milan ahead before Fede Dimarco's equaliser, but defender Matteo Gabbia headed home the winner in the final minute.
“Of course Milan are a very good team. They did better than us this evening and deserved the victory,” Inzaghi told DAZN.
“We had the wrong approach and weren’t enough of a team, which is rare for us. We didn’t start either half with the right attitude, I tried to change a few things, but it didn’t help the situation.
“We weren’t solid, we lost our shape and allowed too many through balls. There was a spell after we equalised for about 20 minutes when we had several more scoring opportunities, but then we came out for the second half with the same wrong attitude as the first. That was decisive, we weren’t working as a team enough.”
Inzaghi continued: “I don’t think we were sharp, as we were making the wrong choices, both in possession and out. The two goals we conceded show that clearly. Milan went clear on goal twice in the first few minutes.
“We had to do more and I as the coach have to take responsibility. We realise this is a derby and we never gave the sensation that we were a team, which has been rare over the last three years,” continued Inzaghi.
“When you concede on a free kick, knowing that Gabbia is good in the air, these details make the difference. I had the sensation we were running on empty mentally more than physically. We can only try to take something positive from a painful defeat and learn from this on how to improve.”