Solskjaer was already under fire due to United's poor recent form, but calls for his dismissal have grown louder following a humiliating home defeat to their arch-rivals.
As Liverpool added insult to injury, Salah completed his hat-trick after the half, becoming the first opposing player to score three goals at Old Trafford for the Reds.
Following the game, Solskjaer was asked about his future at the club amid increasing pressure from supporters.
"No [doubt about being the right man to manage United] - we've come too far as a group," he told Sky Sports.
"We're too close to give up now. It's not easy to say something apart from it's the darkest day I've had leading these players.We were good enough, individually or as a team," said Ole
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