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The Reds highlighted the massive gulf between the two sides, as Mohamed Salah's hat-trick and a goal each from Naby Keita and Diogo Jota secured a sensational victory for the Merseysiders.
Solskjaer's job is now under severe scrutiny after a series of unconvincing performances, and this result now leaves them eight points adrift of league leaders Chelsea with only nine games played so far this season.
While the Norwegian's coaching qualities are being brought into question, his character as a person cannot be disputed after doing the last thing anyone would want to do after such a chastening result.
GiveMeSport reports how the legendary ex Red Devils striker still took the time to sign autographs and pose for pictures with United fans, who still appeared to be in good spirits despite the recent horror show on the pitch.
Solskjaer is not giving up on the fight though and believes the only way is up after a heaviest-ever home defeat to their arch rivals.
"We know we are rock bottom; we can't feel any worse than this. Let's see where we take it," he told Sky Sports after the game.
"I have come too far; we have come too far as a group. We are too close to give up now. "It is not easy to say something apart from it is the darkest day I have had leading these players.
"We were not good enough individually and as a team - you can't give a team like Liverpool those chances, but unfortunately we did.
"The whole performance was not good enough. We created openings, they had chances and they have been clinical. The third goal decided the game."
United will be hoping to bounce back on Saturday when they take on Spurs at the Tottenham Hotspur Stadium, before continuing their Champions League campaign a week on Tuesday with a trip to Atalanta.
Their next home game will see reigning champions Manchester City visit Old Trafford on 6th November.
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