Fred was remarkably fortunate to escape a straight red card midway through the first-half, when he appeared to headbutt PSG midfielder Leandro Paredes, only for referee Daniele Orsato to consult the pitchside monitor and decide that a yellow card was sufficient punishment.
"Fred shouldn't put his head towards him [in the first half],” Solskjaer conceded afterwards. “I don't think he touched him. He was a bit lucky to stay on."
Despite the close shave, the Brazilian did not ease off and might have been sent on his way before the break after another challenge with Paredes.
Solskjaer had the likes of Paul Pogba and Nemanja Matic available on the bench, but persisted with the Brazilian. He was finally given his marching orders on 70 minutes, ironically in harsh circumstances, shown a second yellow after appearing to win the ball with a fair tackle on former United man Ander Herrera.
The result leaves United needing a result away at RB Leipzig on the final day of the group stage to progress, and when asked about what could prove a costly decision not to hook Fred at half-time, Solskjaer 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,” he added. “Ander [Herrera] knows that."