Jurgen Klopp gives instructions to Jordan Henderson. Photo: Michael Regan/Getty Images
Mohamed Salah scored a hat-trick - to take his goal tally for the season to an incredible 15 goals in 12 appearances - to help secure the historic win after strikes from Diogo Jota and Naby Keita had put the Reds 2-0 up in the opening 13 minutes.
Jurgen Klopp’s reaction to ‘historic’ win
"I got told that it never happened before in the history of LFC. This group always wanted to write their own chapter so this was a little chapter tonight,” said Klopp.
"People will talk about it in the future because it won’t happen again in a long time, if ever."
He added: "We saw the game and we were lucky in two or three situations in the first half when United could have scored - they should have scored the first one (which fell to Bruno Fernandes) but it doesn’t make our performance smaller.
"In front of the goal, in the last third, we were exceptional. Clinical and ruthless, the high press was outstanding, formation top, all these things you want to see as a coach.
"The difference is you don’t usually score in each situation and we did."
“The result is insane,” Klopp added. “It is special but we don’t celebrate like crazy, we have respect for the opponents.”
Klopp continued: "Second half, early 5-0 and the red card - game over, so just control it and try to get home healthy.
"I am not sure 100 per cent that worked out because Millie is injured and Naby as well. We have to see how serious it is. It is very painful but we will see."
Klopp also initially thought Cristiano Ronaldo’s challenge on Curtis Jones at the end of the first half warranted a red card.
"I saw it, of course, and it looked like a red card but I got told he hits the ball or didn’t hear the whistle," Klopp said.
"I don’t want Cristiano getting a red card. For me it looked like (a red) but I got told it was not and that’s fine."
Jordan Henderson hails “big step forward”
Liverpool captain Jordan Henderson was delighted with his side’s performance and said he was running out of words to describe just how good Mo Salah is.
“Old Trafford is a tough place to come, I’ve been here many times. So, overall I thought it was a fantastic day,” Henderson Liverpoolfc.com.
“A great performance from start to finish. A clean sheet, which is really important for us. And obviously some amazing goals as well. So, a really pleasing day and a big step forward.”
Asked about Salah and his incredible run of form, Henderson said: “Incredible. Nothing really I can add but he is a special player.
“Hopefully he can stay in this run of games for a long, long time and keep scoring goals, keep working hard for the team and keep playing the way he is because he is a big bonus for us at the minute.”
What’s next for Liverpool
The Reds are in Carabao Cup fourth-round action when they travel to Preston North End on Wednesday.
Klopp’s men are then back at Anfield when they host Brighton & Hove Albion on Saturday, 30 October (15.00).