The Champions League may offer their best way back into Europe’s elite club competition as they are well off the pace of the top four but Klopp is not getting ahead of himself.

Asked whether it was a ridiculous notion to think about winning the trophy for a seventh time he said: “It is kind of – but the only reasons you play in this competition is because you want to win it.

“But we aren’t silly and so far this season it is not one which looks like we will win the Champions League in the end.

“We have to wait for the draw and it will be an extremely tough game whoever we get.

“We don’t really think that far, we think about from tomorrow and about Wolves (on Monday).

“We had momentum in that (the Champions League) but not in the Premier League yet and we will have games to get that back – and that would help the Champions League definitely.”

Key to the relative ease of victory in Budapest was the restoration of Fabinho to central midfield for the first time since he was forced to permanently deputise at centre-back when Virgil Van Dijk’s season was ended by a knee injury in the Merseyside derby in mid-October.

But central defender Nat Phillips, on his European debut having been omitted from the squad for the group phase, was also outstanding at the back.

“It was my hope for the season and during the season (to play the Brazilian in midfield) but it didn’t happen so we have to see what solutions we can find the next few games,” Klopp added.

“Of course, number six is his best position, he is one of the best in the world in that position that is clear: not only defending-wise but creating as well.”

On the 23-year-old Phillips, who looked to be heading out of the club in September, the Reds boss added: “Oh my God. What a boy he is, what player he is, what a night it is for him. That’s absolutely great.

“The concentration level he shows now week in week out since he is playing for us is absolutely incredible.

“He is doing exactly the right things at the right moment. In the air he is a monster and you could see today football-wise he is not bad. I couldn’t be happier for somebody more than I am for Nat at this moment.

“Not a lot of people get the honour to play a Champions League game and he has that now and he played a really good one and he won it and qualified for the last eight. That is really special.”

There was no expected spirited comeback from the Bundesliga’s second-placed side and coach Julian Nagelsmann accepted their performance did not warrant progress.

“I think we deserved to be knocked out. I think the emotional qualities we’ve had in recent matches in the league and cup weren’t shown today,” he said.

“We don’t like losing but sometimes you have to admit the opponent was better.

“We are angry and sad but we’ll focus on Frankfurt who we play in the Bundesliga. It is well-deserved Liverpool go into the next round.”