Fred was sent off in the 70th minute of the European contest, having picked up a second yellow card for a challenge on Ander Herrera, where the Brazilian appeared to win the ball.
The midfielder was handed his first booking for moving his head towards Leandro Paredes in the first half, and Solskjaer admitted that the 27-year-old was fortunate not to receive a straight red for the incident.
The Norwegian has revealed that he considered replacing Fred at the break but suggested that he did not want to withdraw the South American due to his impressive form in recent weeks.
"Yeah [I considered it]," he told BT Sport. "Fred has played really well. We spoke about staying calm and on your feet.
"The second yellow card was nowhere near a foul. Ander knows that. Fred shouldn't put his head towards him [for the first yellow]. I don't think he touched him. He was a bit lucky to stay on."
United ultimately suffered a 3-1 defeat to PSG and now need a point in their final group game away to RB Leipzig next week to ensure that they progress to the last-16 stage of the Champions League.