Inter took a comfortable 2-0 lead before the breakthrough goals from Marko Arnautovic and Davide Frattesi but relied on Sommer to save the three points later in the game.
"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," Inzaghi told DAZN.
"After that, we lost our lucidity, against a team like Udinese that has always shown interesting things."
The Inter coach was sent off in stoppage time, having seen his second yellow card of the night after losing his cool and entering the pitch with heated gestures towards the referee.
"I made a mistake at the end, I apologised to the referee," Inzaghi said.
"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."
Inzaghi was booked for the first time just after the restart for his complaints when Inter striker Marcus Thuram was brought down on the edge of the box by an opposition player.
He will sit out Inter's trip to Parma on Saturday, while the team will be missing some important players when they face AC Milan in the first leg of their Coppa Italia semi-final on Wednesday.
"At the moment, we are in difficulty. Of our five substitutions, four were forced," Inzaghi said.
"Arnautovic and Frattesi took two knocks and had to be changed, (Federico) Dimarco and (Matteo) Darmian had (only returned following injuries). On Wednesday, we will also have (Kristjan) Asllani suspended.
"It would have been the fourth full match for (Hakan) Calhanoglu, and I preferred to take him off."
Inzaghi added that forwards Mehdi Taremi and Lautaro Martinez, as well as defender Denzel Dumfries, will not be available against Milan.
"We will move forward hoping they can give us a hand in the future because we will need them as we progress in the competitions. Then the Club World Cup will be important for us," the coach added.