The Serie A giants endured a desperately disappointing 2013-14 campaign and finished eighth in Italy's top flight.
Former Milan midfielder Clarence Seedorf took over as head coach from Massimiliano Allegri in January, but the Dutchman has subsequently been replaced by his former team-mate Inzaghi at San Siro.
Inzaghi has promised supporters a team they can be proud of, yet erred on the side of caution when predicting how Milan will perform in Serie A this term.
"We came eighth [last season], we need to be patient and I repeat that the Milan fans will be satisfied because we will give everything," Inzaghi said at a news conference.
"The other teams are ahead of us, have consolidated and have new signings. We just need to work and for me to have discovered these boys gives me satisfaction.
"We will try to give everyone a hard time but I don't know where we will finish. After one month of work I can confirm the team has heart. We will win the fans over."
Inzaghi remains confident despite a poor showing in the International Champions Cup in the United States, where Milan lost all three matches and conceded 10 goals.
"I need to do well and bring back the spirit to the team," he added. "I assure you that a lot of the players have an attachment to the Rossoneri.
"If the team sees the staff, the club and coaches working, the players will have to put everything into it too. I have seen all of that in these months. You can't create a winning group in 20 days but we are on the right track."
