Liverpool boss Jurgen Klopp says their 5-0 win at Manchester United was unexpected and "insane".
Mohamed Salah scored a hat-trick either side of half-time after Naby Keita and Diogo Jota had given Liverpool a 2-0 lead in the opening 13 minutes.
The win - which takes Liverpool second, a point behind Chelsea - was their biggest victory at Old Trafford.
"It is a really good day - a big one. This is a little chapter in the history of the club," said Klopp.
He added: "People will talk about it in the future because it won't happen again in a long time, if ever."
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Speaking to Sky Sports, Klopp added: "What can I say? Did I expect that? No.
"The result is insane. It is special but we don't celebrate like crazy, we have respect for the opponents.
"We were lucky in some moments, United are not in their best moment."
'People will stand up and take notice'
The result, which was only Klopp's second win at Old Trafford since becoming Liverpool manager in 2015, means Liverpool remain the only unbeaten side in the Premier League.
Former Premier League striker Dion Dublin, part of the BBC Radio 5 Live commentary team at Old Trafford, said Liverpool's performance was down to Klopp.
"To do what this current Liverpool side has done today at Old Trafford in front of 76,000 fans and embarrass Manchester United as they did, it has to be down to the influence of Jurgen Klopp," added Dublin, who was at United from 1992-94.
"It is how he sets them up, the belief, the hard work. I can't speak highly enough of Liverpool today - they were absolutely brilliant."
Before the season started, champions Manchester City and Chelsea were picked by 20 BBC experts as the two teams to challenge for the league this season, but former Liverpool defender and Sky Sports pundit Jamie Carragher says Liverpool can win the title.
"They are a class apart - this is a special Liverpool team and a special manager," said Carragher.
"I don't think many people thought Liverpool can win the league, but to come here today and win, people will stand up and take notice."
'We need to win the Premier League'
Salah's hat-trick took him to 15 goals in all competitions for Liverpool this season and the Egyptian has now scored in his last 10 games.
He flicked home Keita's pull-back for his first goal, before curling a left-footed effort past David de Gea at his near post in first-half injury time.
His hat-trick was completed when he latched onto a Jordan Henderson through ball and dinked over the advancing De Gea.
"I think it is great to win 5-0 here," said Salah, who is the first opposition player to score a Premier League treble at Old Trafford. "We knew before the game it would be tough if we did not play our game.
"We know what it takes to win the Premier League, we did it two years ago.
"From our heads from pre-season, we need to win the Premier League and hopefully we go for that."
Salah's contract expires in the summer of 2023 and he said this week he wanted to end his career at Anfield.
After the game Klopp said he "knew already" Salah, 29, wanted to stay at the club where he won the Premier League in 2019 - a year after lifting the Champions League.
"He enjoys his football and long, long, long, may it continue," added Klopp, whose side also recorded their biggest win over United since a 5-0 success at Anfield in 1925.
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