The Rossoneri take on city rivals in Inter in the 162nd Milan derby on Sunday, with both having endured disappointing seasons thus far which looks set to see them miss out on European football.
But Inzaghi, who has faced intense speculation that he will be lucky to last past his first season as a head coach, believes he and current president Silvio Berlusconi have what it takes to get the seven-time European champions back on track.
"I want to see a Milan side back at the top and that wins," Inzaghi told a press conference.
"Football goes in cycles, but I am convinced that with this President and the club directors we will go back to the top and win again. I am very happy about the president’s confidence in me and I hope that we can win for him.
"I will continue on my path with the same spirit and always motivated. I have only just started my coaching career, I am very calm and will continue on this path. I hope to repay all of the faith that has been shown in me."
Milan trail Inter in the derby head-to-head by 60 wins to their 50, have won only one of their last seven games against Inter in Serie A (losing four), and have managed just two wins in their last six league games.
But Inzaghi says he has seen enough positives from his side to believe they can emerge victorious following last week’s 1-1 draw at home to Sampdoria.
"It is important for the league table and that’s not all. We’re taking on a great side, but we have to take to the pitch convinced that we can give a top performance," he said.
"Against Sampdoria we had 24 shots on goal. From those, 7 were on target but only one was a goal, which means that we have to improve… I am calm ahead of the match but it’s clear that the derby is a match that has to be won."
Inzaghi also revealed he was hoping to welcome back Keisuke Honda, who has been out with a foot injury since the middle of March.
"Honda has recovered," Inzaghi said. "He has been training since Tuesday and he has recovered 10 days ahead of schedule.
"In the final training session, I will see whether to start him or not. He still feels a bit of pain when he strikes the ball hard, but it’s normal."
Milan sit ninth in Serie A - seven points behind Fiorentina and a Europa League berth - just one point of Inter in tenth.