Thomas Tuchel’s French champions came out on top in a controversial affair, with Marquinhos seemingly in an offside position when he moved them 2-1 ahead late in the second half.
Just a minute later things went from bad to worse for United as Fred picked up a second yellow card for a challenge on Ander Herrera, despite replays appearing to show him winning the ball.
Nevertheless, the Brazilian arguably received his comeuppance having somehow avoided a straight red for an apparent headbutt on Leandro Paredes in the first half.
While contentious refereeing decisions are likely to dominate the headlines, United will be scratching their heads as to how they failed to go in front during a dominant early second-half spell.
After Marcus Rashford had cancelled out Neymar’s opener, Anthony Martial blazed the ball over from close range and Edinson Cavani struck the cross bar.
The hosts were made to pay in the end, as Marquinhos’ strike and Neymar’s second of the game sealed a sensational night’s work for PSG.
And in his post-match interview, Solskjaer admitted United were punished for squandering a number of golden opportunities.
“It was a very good game which deserved fans. With a bit more clinical finishing we should have finished the game. They were there for the taking,” he told BT Sport.
“We had some big chances. The difference when you get to the big games is the clinical moments.
“If Marquinhos had bigger studs on he'd have been offside. It's marginal. You can't really put your finger on the deciding factors.”
When asked about Fred avoiding a red card in the first half, Solskjaer said: “Fred shouldn't put his head towards him. You don't do that. He's a bit lucky. It's either nothing or a red card.
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“Yeah [I did consider taking him off at half-time]. But Fred has being playing really well. Played really well.
“We spoke about staying calm. Staying on your feet. The second yellow card is nowhere near a foul. Ander knows that. He definitely knows.”