The Reds were completely outplayed in their Champions League Group A opener at the Stadio Diego Armando Maradona on Wednesday night, suffering their joint worst defeat in the competition as they were blown away 4-1.
Victor Osimhen, Piotr Zielinski, former Fulham midfielder Andre-Frank Zambo Anguissa and Giovanni Simeone - son of Atletico Madrid boss Diego Simeone - were all on target in Naples, while the hosts also spurned several other glorious chances and Osimhen saw a penalty saved by Alisson after Virgil van Dijk’s clumsy foul.
Luis Diaz’s second-half strike was a rare highlight for Liverpool, who have now won only two of their first seven matches of the season across all competitions.
As well as needing to recover their Champions League form after losing in last year’s final, Klopp’s side are already well off the pace in the early Premier League title race, sitting seventh and six points adrift of early pacesetters Arsenal.
Thomas Tuchel’s surprise departure from Chelsea on Wednesday further underlined that past success does not guarantee managers much staying power at top clubs in the cut-throat world of modern football, but his fellow German does not fear a similar fate at Anfield, insisting that Liverpool owners Fenway Sports Group (FSG) are more patient than the new Blues regime under Todd Boehly and Clearlake.
“Not really but who knows,” Klopp said when asked about worries over his future. “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.”
Klopp is under no illusions as to the situation Liverpool currently find themselves in and called for his side to “reinvent themselves” to escape tough waters with Wolves, Ajax and Chelsea still to come this month and difficult tests against the likes of Arsenal and Manchester City looming during a packed October schedule.
"You don't think a lot after the game, you react more," he 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."