The 47-year-old has taken responsibility for his "stupid" behaviour in the loss to the Partenopei, in which he was sent to the stands
The 47-year-old coach was sent off for gesticulating angrily at the fourth official after he refused to allow Neven Subotic to return to the field of play following a head injury.
However, Klopp has taken full responsibility for his behaviour in the loss to Rafael Benitez's men - but believes victory was there for the taking.
Speaking to ZDF, he said: "We did not show our prettiest face tonight, yet we lost with the closest of defeats.
"We know now that we can beat Napoli, but too many things went wrong, including my red card. It was stupid and I acknowledge that.
"I behaved like a monkey out there. I went too far."
Last year's beaten finalists went behind to a Gonzalo Higuain goal on 27 minutes, with Lorenzo Insigne doubling the advantage midway through the second half before Juan Zuniga netted an own goal three minutes from time.