The Red Devils took the lead in the first half through Daniel James’ excellent finish into the top corner.
However, Solskjaer’s men were pegged back in the second half when Jannik Vestergaard headed home an equaliser for the hosts.
Manchester United were unable to find a winner despite the hosts having been reduced to 10 men for the closing stages.
Pogba completed 50 of his 62 passes at St Mary’s and was guilty of giving the ball away on a number of occasions.
And Solskjaer admitted that Pogba and a handful of his team-mates did not perform at their best in the closing stages of the game.
Speaking in an interview quoted by Metro, Solskjaer said: “I think we as a team after about half-an-hour started giving sloppy balls away and Paul was one of them. He wasn’t any different to anyone else.
“We as a team didn’t play well but in the last 20 minutes or half-an-hour, he did create loads for us going forward.
“Everyone expects everything from him every game, he has to defend, he has to attack, he has to win headers, he has to dribble past people, he has to make passes.
“That’s just Paul and he’ll thrive on that.”
Manchester United have taken just five points from a possible 12 in their opening four games in the Premier League this season.
They will attempt to return to winning ways after the international break when they take on Leicester City in front of their home fans on Saturday 14 September.
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