Fresh from back-to-back losses at Udinese and at home to Genoa, the Rossoneri saw their hopes of ending a five-game winless run all but end after just 45 seconds of action at the San Paolo, with Mattia De Sciglio seeing red for a professional foul on Marek Hamsik.
Inzaghi was reluctant to be drawn on his job prospects but suggested that it would be unfair if a game in which his side had to play over 89 minutes with 10 men would be a factor in determining his future.
"I have been able to turn everything around since taking charge last summer," the Rossoneri coach told Sky Sport. "We had four great months and then we struggled.
"But there's something good there. The club will make their evaluations but I have a contract.
"But it was a game shaped by the dismissal. I saw a good team for 70 minutes. Maybe a yellow would have been fairer than a red, because Gabriel Paletta was also there.
"We fought hard with 10 men. I can't say anything bad about our spirit.
"We even had a chance to score through Bonaventura when the midfielder grazed the post with a header in the first half. We definitely didn't deserve to suffer such a heavy defeat."