Liverpool's 'Fab Four' shone in a 7-0 trouncing of Spartak on Wednesday, with Philippe Coutinho scoring a hat-trick, Sadio Mane claiming a double and both Roberto Firmino and Mohamed Salah finding the net.
But having seen his team crash 4-1 at Tottenham Hotspur after thrashing Maribor 7-0 earlier in the group phase, Klopp is desperate for his men not to ease up ahead of Sunday's derby clash with Everton.
"We showed tonight that we learnt from the mistake we made in Seville," Klopp said, referring to Liverpool's 3-3 draw against Sevilla on their previous Group E outing, when they had squandered a 3-0 lead.
"Now we have to show that we learnt from the mistake we made after Maribor when we faced Tottenham. We will be ready again on Sunday and if the crowd are ready to help us, it would be nice again."
A brace from Coutinho, the first a penalty, and an opportunistic Firmino strike put Liverpool 3-0 up inside 18 minutes and they turned the screw after half-time.
Mane and Coutinho struck in quick succession, the latter completing his first Liverpool hat-trick, before further neatly worked goals from Mane and Salah took the team's goal tally to 32 in nine matches.
Klopp could not disguise the extent to which he had enjoyed watching his team, saying they had scored "fantastic goals, unbelievably nice goals", but there was an accompanying note of caution.
"We should not think it will be like this from now on until the end of our entire lives," he said.
Emre Can received a booking that rules him out of the first leg of Liverpool's last-16 tie and Klopp admitted an injury that forced left-back Alberto Moreno to limp off in tears had further dampened the mood.
"We come to the little shadow tonight that Alberto Moreno needed to get substituted," said Klopp.
"It was a strange situation. He's a tough guy and if he cannot continue the game, then we should consider it could be something serious.
"In the treatment room he was a little bit more positive, so maybe we are lucky and it's not too serious."