Mohamed Salah scored a hat-trick as Liverpool humiliated United and piled the pressure on Solskjaer.
Gary Neville said the result puts Solskjaer under “untold pressure” but the United boss insisted he has no doubts that he is the right man for the job.
“No,” said Solskjaer speaking to Sky Sports. “I have come too far, we have come too far as a group. We are too close to give up now.
“You can look at last season we lose to Spurs 6-1. This is worse, miles worse. This is miles worse for me as a Manchester lad.
“I have just got to say we have to get over this as quickly as we can. It is going to be a difficult one. The players will be low but there is loads of characters there.
“We know we are rock bottom, we cannot feel any worse than this. Let’s see where we take it. 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.”