The France international made his move to San Siro from Valencia permanent in the close-season, but did not feature in the opening day win over Lazio.
Inzaghi introduced Rami off the bench for the final 28 minutes of Sunday's remarkable 5-4 Serie A win at Parma and the 28-year-old is confident further first-team opportunities will present themselves.
"The important thing is that we showed we're a team," he said.
"It's true that since I was a child I've loved this club and these colours.
"If I'm on the bench, I don't feel less important, I know I can have my chances.
"We haven't forgotten last season where we did badly, we're working hard and we will continue to do so to take Milan back to being a great club.
"Coach Inzaghi is pushing us to do so as well."
Pep Guardiola issues a very blunt answer when quizzed by reporters on latest accusation levelled against Manchester City
'I think my opinion is more important than Roy Keane's. I know as a captain he does things sometimes with his arms, criticising his team-mates, but most of all it's a bit of frustration.' - Ruben Amorim hits back in Bruno Fernandes row
