Fred was sent off after a challenge on former United teammate Ander Herrera.
Solskjaer remarked after the Champions League defeat: "Yes, that's not a yellow card, we know that. The referee, when he sees it, he knows he's made a mistake. That's something that sometimes happens. You can't do anything about it unfortunately, but it was a clear and obvious error.
"Very frustrating. [It's] a clean challenge, a fair challenge. He played really well. Fred is so energetic out there. He'll hold his hands up and say sorry, but you can't be sorry for winning the ball, can you?"
On his apparent head-butt on PSG midfielder Leandro Paredes, Solskjaer insisted: "Fred shouldn't put his head towards him. You can't do that. So he was a bit lucky. I thought it was either nothing or a red card. I thought he was maybe a bit lucky to stay on when the referee decided to give him anything."