Manchester United s Norwegian manager Ole Gunnar Solskjaer (L) and Liverpool s German manager Jurgen Klopp (R) look on during the English Premier League football match between Manchester United and Liverpool at Old Trafford in Manchester, north west England, on October 24, 2021. AFP
United trailed 4-0 at half-time for the first time in Premier League history as Mohamed Salah struck twice after Naby Keita and Diogo Jota opened the floodgates inside the first 15 minutes.
Salah completed his hat-trick shortly after the break as Liverpool won by a five-goal margin for the first time away to their fiercest rivals.
"It is not easy to say something apart from it is the darkest day I have had leading these players," Solskjaer told Sky Sports. "We were not good enough individually and as a team.
"The whole performance was not good enough."
Solskjaer's men have taken just one point from the last 12 in the Premier League to fall eight points off leaders Chelsea after just nine games.
United were thrashed 6-1 at home to Tottenham in front of an empty Old Trafford last season, but recovered to finish second in the Premier League.
However, Solskjaer said this defeat was even more damaging given the context of the rivalry between the clubs.
"You can look at last season we lose to Spurs 6-1 this is worse, miles worse," he added.
"This is miles worse for me as a Manchester lad. I've just got to say we have to get over this as quickly as we can."
Solskjaer is yet to win a trophy since taking charge in December 2018, but has been credited with leading the club back into the Champions League in the past two seasons.
And he insisted he will not step down despite the growing calls for him to lose his job.
"I have come too far, we have come too far as a group. We are too close to give up now," he said.
"The players will be low but there's loads of characters there.
"We know we are rock bottom, we can't feel any worse than this. Let's see where we take it."
United captain Harry Maguire issued an apology to the club's fans for the humiliating defeat.
"We apologise to the fans, it was nowhere near good enough for this club," said the England defender.
"To lose to Liverpool in any game of football hurts. The way we lost the game, to be 4-0 down at half-time in front of our fans, like I say it is not good enough."
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