The trip to Napoli always looked like the toughest test of a group that also includes Ajax and Rangers, but few could have foreseen the error-strewn display that would unfold at the Stadio Diego Armando Maradona.
Piotr Zielinski, Andre-Frank Zambo Anguissa and substitute Giovanni Simeone scored in a first half that Liverpool were fortunate to end only three goals behind.
Victor Osimhen had seen a first-half penalty saved shortly before Virgil van Dijk denied Khvicha Kvaratskhelia on the line, with Zielinski scoring against the start of a second half on a night when Luis Diaz struck a consolation.
"You don't think a lot after the game, you react more," Liverpool boss Klopp said.
"We have to kind of reinvent ourselves because basic things were not there. It's a difficult period, no doubt about that.
"If you're not playing exceptionally well, you still can defend on a really high level. We should be able to do that.
"The start of the game doesn't help. If we want to defend better and concede a penalty after three minutes and the next one, obviously you cannot exactly do that. Tonight we were caught in-between.
"But, still, it's the job to do. That's what I mean. It's not that we have to reinvent a new kind of football.
"You always try to improve but in this moment obviously everybody would be happy if we could just play similar stuff to what we used to play."
The loss even led to a question as to whether Klopp worried about his future given Thomas Tuchel's sacking by Chelsea earlier in the day.
"Not really but who knows," Klopp said after the Group A opener. "The difference obviously (is) they are different kind of owners.
"Our owners are rather calm and expect from me to sort the situation and not thinking that someone else should sort it.
"That's how they always saw it and on the day when they change their thoughts then they might tell me."