The defeat further dented Milan's slim European hopes, with Inzaghi's men sitting six points adrift of Fiorentina in sixth place - which is likely to be enough to seal Europa League football due to Juventus and Lazio's presence in the Coppa Italia final.
The Rossoneri coach has tried to defend his players' poor performances in recent months but slammed the attitude of his team after the game and demanded a response on Wednesday against Genoa.
"The objective is to earn our place at Milan," Inzaghi told Sky Sport. "This was a bad performance and I was extremely angry at the attitude I saw.
"There are no excuses. In the other games Milan had always tried to fight, but this time I saw nothing. It looked like Udinese were playing a Champions League final compared to us.
"I can only apologise to the fans. Thankfully we'll be playing again in a few days and we must wipe this performance from the memory as soon as possible.
"If I could've made 10 substitutions at half-time, then I would've done. I have little else to say. We are Milan and cannot embarrass ourselves with a performance like this."