United Kingdom - Liverpool manager Jurgen Klopp warned his side will still have to "work like hell" to reach the Champions League semi-finals despite taking a commanding 3-0 quarter-final first leg lead over runaway Premier League leaders Manchester City.
City lead Liverpool by 18 points in the Premier League, but their only league defeat this season came in a 4-3 thriller at Anfield in January, and they suffered an even worse fate on Wednesday to leave their hopes of winning the European Cup for a first time hanging by a thread.
Just as in the January meeting between the sides, the prolific Mohamed Salah, Alex Oxlade-Chamberlain and Sadio Mane were on target for the hosts.
"We beat the best team in the world so that's a really good performance," said Klopp.
"It was good tonight, but I am not interested in being good. In this competition it is about going to the next round, and we are not in the next round. Let's talk about it after the next game.
"We will really have to work there again like hell."
Klopp's caution is born out of the fact that City thrashed 10-man Liverpool 5-0 in their only previous meeting at the Etihad this season.
"We conceded there already five. How can I say it is not possible?"
And City boss Pep Guardiola insisted he still believed despite his side's most comprehensive defeat of the campaign.
"I think in this room there is nobody except the guy talking to you who believes we are going to go through," said Guardiola.
"Tomorrow we are going to try to convince ourselves that in six days it is 90 minutes more and we are going to try."
Liverpool's night was slightly marred when Salah limped off with an injury early in the second half.
"After the game he said: 'I will be good, I will be fine' but now we have to wait for the real diagnosis," added Klopp on his Egyptian star's fitness.
City could already be crowned English champions by the time the sides meet again for the second leg in six days' time should they beat local rivals Manchester United on Saturday.
Guardiola's side have been in stunning form for the large majority of the season, but he lamented a poor 20-minute period in the first-half that has likely cost them a shot at European glory.
"The result is tough but I don't have feeling we played to concede that result," added Guardiola. "But in this competition (what happens) in the boxes makes all the difference and they were so good in those situations."
City were well aware of the cauldron they were facing from the off as their team bus was battered by bottles and cans on their arrival at Anfield.
Klopp was quick to apologise as were the club in a strongly-worded statement condemning the actions of their own supporters.
The atmosphere was equally electric inside the stadium for Liverpool's first Champions League quarter-final for nine years.
The visitors were caught out on the counter-attack on 12 minutes when Salah sprang Roberto Firmino in behind the City defence and, after his initial effort was parried by Ederson, Firmino teed up Salah to smash home his 38th goal of the season.
City should have struck back straight away when Leroy Sane pulled his shot wide from the edge of the box as City outnumbered the Liverpool defence on a quick break of their own.
However, they were soon swept away in the euphoria engulfing Anfield as Oxlade-Chamberlain pounced on a loose ball on the edge of the area and rendered Ederson helpless with a stunning strike from 20 yards.
A third duly arrived as Salah stood up a cross to the far post for Mane to head in and take Liverpool's prolific front three's tally for the season to 77.
City pressed relentlessly for an away goal that would get them back in the tie, but failed to register a single shot on target as Liverpool held out for a priceless clean sheet.