Klopp saw most of his team's game from a stadium TV after he was sent off in the 30th minute for an angry outburst at the fourth official following Napoli's opening goal.
Klopp was furious with the fourth official for not letting defender Neven Subotic back onto the pitch sooner after an injury break, allowing Napoli to score in the process.
"I apologised immediately after the game to my team, the fourth official and the referee as well," Klopp told reporters. "I have to accept the consequences for my actions. I was like a monkey out there. That was stupid.
"My emotions turned a well-run game into a hectic affair."
Passionate Klopp, who led Dortmund to back-to-back Bundesliga titles in 2011 and 2012, is known for his occasional outbursts on the touchline and has been repeatedly ejected from domestic matches.
"I did not show my prettiest face out there. I told myself I did not want to see such pictures of me again and I thought I could do it. It was absolutely my mistake."
Dortmund, last season's Champions League runners-up, also had keeper Roman Weidenfeller sent off for handball outside his box.
Klopp blamed himself for the red card, saying his emotional behaviour did not help calm his players down.
"That was also on me," he said. "I just could not calm down and so the team were more stressed. So I also have my share in Roman's red card, because if we are calm then these things do not happen."
- Sports & Recreation