After falling behind to a Neymar opener, United could have been reduced to 10-men midway through the first half when Fred appeared to headbutt midfielder Leandro Paredes.
After a VAR review, the referee decided to give Fred just a yellow card but that meant the Brazilian was walking a tightrope with an hour left on the clock.
Solskjaer somewhat bizarrely decided to leave the midfielder on for the second half and the inevitable happened following Marquinhos’ goal twenty minutes from time when Fred was sent off.
The former Shakhtar Donetsk midfielder appeared to win the ball before following through on former Manchester United midfielder Ander Herrera and Solskjaer says the Spaniard ‘knows’ it wasn’t a foul.
Fred shouldn’t put his head towards him [for the first yello],’ said Solskjaer.
‘I don’t think he touches him but still you don’t do that. So yeah he’s a bit lucky. It’s either nothing or a red card. I thought maybe he was a bit lucky to stay on once the referee gave him anything.
Asked if he thought about subbing the Brazilian at half-time, Solskjaer said: ‘Yeah, yeah but Fred has played really well.
‘We spoke about staying calm, staying on your feet and the second yellow card is nowhere near a foul. Ander knows that as well. He definitely knows.’
They travel to RB Leipzig next week needing at least a point to progress to the last-16 but they will likely need a win to come top of the group.
Fred will be suspended for the trip to Germany.