Liverpool lost 2-1 thanks to a 96th-minute own goal from Joel Matip.

“Something like this never happened, so that is why I think a replay is the right thing to do,” said Klopp.

BBC Sport understands there is no prospect of the Premier League considering a replay and it is unclear whether there has been a formal request from Liverpool.

Asked whether the club had asked – or would ask – the Premier League for a replay, Klopp said: “At this stage we are still going through the information we have.”

Referees’ body PGMOL released the audio of discussions between the match officials over the offside on Tuesday.

In the audio, England says the check is “perfect” before swearing when he realises a mistake has been made.

Klopp said: “The audio didn’t change it at all. It is an obvious mistake. There should be solutions for that. The outcome should be a replay. But it probably won’t happen.

“The argument against that would be it opens the gates. It is unprecedented. I’m used to wrong and difficult decisions, but something like this never happened.”

After releasing the audio, PGMOL said the error was a result of a “lapse of concentration and loss of focus”.

The controversy has prompted a debate about the use and efficacy of VAR.

The Premier League added that the incident in Saturday’s game, and the subsequent review of what led to the incorrect decision, highlighted “systemic weaknesses in the VAR process”. The league plan to undertake a comprehensive review alongside the referees’ body to “seek consistently higher standards of VAR performance”.

Although Klopp said the mistake was not made “on purpose”, he added: “These things should not happen. Other mistakes should not happen. Find a solution to deal with it.

“We rush them and we get a quick decision, but the wrong decision.”

Klopp said it would have been better to correct the mistake once it had been realised and said he wants a protocol put in place to avoid similar problems again.

He said: “If that would happen again, I would say replay. Or much, much better than a replay – sort it in that moment. Common sense.”

There is no precedent in the UK for a result to be changed or a game to be replayed because of a refereeing error.

A 1999 FA Cup third-round tie was played again after Arsenal manager Arsene Wenger offered Sheffield United a replay following a controversial winning goal in the first game.

The officials involved in the match at Tottenham Hotspur Stadium have not been selected for this weekend’s Premier League games, with England and Cook stood down for the rest of last weekend.

The on-field referee at Tottenham-Liverpool, Simon Hooper, will be the VAR for Bournemouth’s trip to Everton on Saturday, while Michael Oliver, who was the fourth official, will feature in two games this weekend.

“I am not angry with anybody at all,” said Klopp. “They made a mistake and they felt horrible that night, I am 100% sure. That’s enough, for me. Nobody needs further punishment.”

Diogo Jota and Curtis Jones were sent off against Spurs. Liverpool failed with an appeal against Jones’ red card for a challenge on Yves Bissouma and he will serve a three-game ban.

“The ref got called to the screen and saw for the first three seconds a frozen picture. I would give immediately a red card for that picture,” said Klopp.

“Then he sees the replay in slow motion. I would have given a red card for the slow motion, but in real time it is not a red card.

“You appeal it then the FA panel tells you ‘no, it is not a clear and obvious mistake’ and I think it is.

“The ref’s first decision was yellow. The clear and obvious mistake is showing a frozen picture and a replay in slow motion.”

Crisis of confidence in VAR – analysis

Dan Roan, BBC sports editor

If the PGMOL thought the release of the audio recordings during the offside fiasco would help to defuse arguably one of the biggest officiating crises in Premier League history, it was mistaken.

Klopp’s suggestion that there should be a replay ensures the debate will now reignite.

Many fans will have sympathy with Klopp over a mistake that could end up costing his team dearly, both in terms of points and financially.

But others will fear such a move could open up a sporting and legal minefield, with rival clubs demanding their own replays over other injustices. Where would it end? What would the threshold be for a replay?

Regardless, the release of the audio recordings has helped fans to understand the mistakes, confusion and panic that unfolded behind the scenes at Stockley Park.

But the shambolic miscommunication, sense of chaos and general lack of composure that comes across is also hugely embarrassing for the authorities given the league’s global status, and raises as many questions as answers.

While PGMOL blamed “significant human error” in the aftermath of the match, the Premier League now accepts that the episode has also revealed “systemic weaknesses” with VAR, a very significant admission.

So when will the PGMOL’s “key learnings”, such as “enhanced clarity of communication”, be introduced, and are they enough?

How will the standards of officiating be improved? If automated offside is to be brought in, when will that be?

Does the International Football Association Board need to reconsider the rule that games cannot be stopped once play has resumed – even if a mistake is made?

And has the time come for much more transparency, with a live audio feed to be made available to fans and broadcasters, as in other sports?

The answer to these questions will dictate whether faith can be restored amid a serious crisis of confidence in VAR.