Playing in front of a sparse crowd, after Milan's ultras called for a boycott prior to kick-off, was not ideal for Inzaghi's side, but they overcame their early nerves to secure a much-needed win.
With the head coach's job reported to be at stake, two goals from Jeremy Menez, plus Philippe Mexes' first of the season, eased some pressure and Inzaghi hopes Milan can use the win as a building block.
"I know that I have to prove myself, as Milan looked to a young coach in a difficult moment," he told Sky Sport Italia.
"I see a club with a strong squad and very experienced players, who are still struggling.
"I knew full well that it wouldn't be easy but I want to see a Milan side that is higher up the standings. We did well until January, then for a series of reasons we lost our way but we're back to creating seven or eight clear-cut chances per game. That's the Milan I like.
"We are not in the position we want to be but I feel the team and club are close to me, we communicate regularly and that is enough for me. I have a contract.
"It's only natural for our fans to be disappointed, so we have to win them back with good performances and results.
"We've seen the Milan of a few months ago and that's something what we can build on."
