Already 2-0 down after second-half goals from Presnel Kimpembe and Kylian Mbappe, Pogba was shown a red card by referee Daniele Orsato after a high challenge on Dani Alves in the 89th minute.
Pogba will now miss the second leg in Paris in a few weeks and Solskjaer gave his view of the tackle after the match.
He told BT Sport: “Paul Pogba is trying to get his body across and Dani Alves is clever enough to put his foot in there.
“Paul wants to shield the ball, he’s unlucky.”
In the history of the Champions League knockout stages, no team has ever managed to reach the next round after a 2-0 home defeat in the first leg.
And former United midfielder Phil Neville says they have no chance of progressing.
He said on BBC Radio 5 live: “I don’t think Manchester United have any chance in Paris [in the return leg].
“PSG have too much European nous, too much class.
“Even though we didn’t see Mbappe at his absolute best, he was still devastating.”
But United midfielder Ander Herrera says the team will remain positive and turn their attention to Monday night’s FA Cup clash against Chelsea.
He told BT Sport: “We are all optimistic and positive – we are building something good.
“Today is going to be a tough night and tomorrow is going to be tough day.
“We are going to fight for the top four and the FA Cup.”