Inzaghi's side lost in the top flight for the first time since September thanks to a Christian Zapata own goal and a Paulo Dybala effort within three first-half minutes.
It was Palermo's first victory on the road in the league since returning to Serie A and ensured Milan slipped to seventh as a result.
Despite the disappointment, former Milan striker Inzaghi believes his squad have shown enough under his tenure to remain positive.
"They were speaking about Milan as the revelation of the season and one match lost cannot change opinions since there are other sides that struggle that were ahead of us last year," he said.
"We have to re-watch the match with a cool head, I didn't get ahead of myself before and I won't get down now.
"I'm disappointed that we've taken a step back. I hope that the players don't lose their self-confidence because it can happen that you lose a match."
Milan's outing was made worse by an injury to Brazilian defender Alex early on, with Inzaghi revealing his replacement Zapata also "felt some pain".
However, the Milan boss stated injuries and fitness issues would not be used as an excuse as Milan's attention now switches to Saturday's clash with high-flying Sampdoria.
"When you lose it's easy to pass on the blame to those on the pitch and the physical fitness, I don't want to fall into this trap," he added.
"I sensed that we lacked the strength to react, this week we can work more and we’ll try and get back on track on Saturday.
"A good coach has to understand what he could have done better. When you lose the coach is responsible, the players gave everything they had, [but] it wasn't enough."
