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 again at the start of a second half. Luis Diaz responded soon after but it was little consolation for the visitors.
“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.
“Tonight was the least compact performance I saw for a long, long time from us… and other teams as well.
“Napoli was really good but we made it easy for them because we lost the ball in areas and then the next situation was a counter-attack. No, that’s not how it should be.
“A few things are really clear, we have to change that, and the reason why it’s now like this is getting a bit more clearer as well.
“But I need time for just saying the right things because at the moment it’s not 100 per cent clear.”
Klopp went over to Liverpool’s travelling fans to apologise following a “very disappointing night” in Naples.
The Reds will be hoping their stuttering start to the campaign has bottomed out with a loss that even led to a question as to whether he worried about his future given Thomas Tuchel’s sacking by Chelsea earlier in the day.
He replied after the Group A opener: “Not really but who knows? The difference obviously (is) they are different kind of owners.
“Our owners are rather calm and expect me to sort the situation and not think 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.”
While wounded Liverpool return home and refocus on Saturday’s home game against Wolves, Napoli fans will celebrate long into the night – even if their head coach is keeping his feet on the ground.
“I think we need to be clear,” Luciano Spalletti said. “Yes, we are very happy, I enjoyed watching this performance first and foremost because Napoli produced a great performance against a top team like Liverpool.
“But I think we need to be clear: we mustn’t get distracted by other situations.
“Above all, you realise just how happy you send the fans home after a game like this. I am very pleased to see the smile on the supporters’ faces but we need to go again.”