Despite his team’s 2-1 victory at Stadio Giuseppe Meazza, the manager was sent off in stoppage time after receiving a second yellow card.
Inzaghi lost his temper and approached the pitch, making heated gestures towards the referee.
Speaking after the match, he admitted his actions were wrong but insisted his team deserved to score two goals.
"I made a mistake at the end, I apologised to the referee," Inzaghi told DAZN.
"Foul on (Joaquin) Correa seemed clear to me, then came the corner kick in which Solet almost scored. "Sometimes adrenaline plays bad tricks, unfortunately, I won't be on the bench next time."
On the result he said: "A splendid first half by the lads, where we deserved more than the two-goal lead.
In the second half, before (Udinese defender Oumar) Solet's goal, we hadn't conceded too much.
After that, we lost our lucidity, against a team like Udinese that has always shown interesting things.