Inzaghi's men have won just one of their last seven fixtures in all competitions and were held to a 1-1 home draw by Empoli in Serie A last time out.
The sequence has seen pressure mounting on the former Italy international, but Inzaghi is confident of turning things around.
"To salvage our season we need to start playing like Milan again," he said on Saturday. "I take things one game at a time.
"At the moment we need to rediscover our identity, confidence and enthusiasm.
"I feel the faith from the president [Silvio Berlusconi] and CEO [Adriano] Galliani every day. The President called me yesterday morning at 8.15 to tell me that he was sorry he couldn't visit.
"They believe in my work and they have also realised that the injuries have penalised us a bit, but this takes nothing away from the fact that we should have done more.
"The president reassures me a lot and for this I thank him. I have a contract with Milan and I know of the respect that the club directors have in me. I will move forwards and then we shall see what happens."
Milan have only managed to attract around 25,000 fans to their last three home matches and Inzaghi believes his side must work hard to increase the numbers coming through the turnstiles.
"It isn't easy to play at San Siro, even if our fans have been very good and patient," he said. "The best medicine right now for us is to give a good performance.
"It annoys me when people say that the players work little, because it isn't true and it isn't right to talk about players that always give their all. I am sad that fictitious things are said.
"We have worked very hard this month to be able to play with greater intensity.
"I'm not looking for excuses, we should have done a lot more, but when we had 90 per cent of the squad available we were third in the league table and I think this counts for something.
"There were many fans during the first match of the year against Sassuolo. It takes very little to win them back and bring them back to the stadium.
"We're not doing that at the moment and we are sorry about it. We need to show the fans what we can do out on the pitch."
Milan host Cesena in Serie A on Sunday.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
