Solskjaer was beaten for the first time in 12 matches as United’s interim manager as second-half goals from Presnel Kimpembe and Kylian Mbappe rocked Old Trafford.
United also had French star Paul Pogba sent off in the final moments, ruling him out of the second leg in Paris next month.
It was a dispiriting evening for Solskjaer, who had sparked such enthusiasm among United’s players and fans since replacing the sacked Jose Mourinho in December 2018.
Solskjaer conceded United, who managed only one shot on target in a tame display, had fallen short of the quality required against top sides like the French champions.
“Yesterday was a reality check for us on the level of top teams. They had the momentum after the first goal and controlled the game,” Solskjaer said.
“You could see that we hadn’t played at this level for a while and we will have to learn.
“It was an experience that can go either way, it’s not going to be a season-defining one, it’s one we have to learn from.”
Pogba’s dismissal was the culmination of a surprisingly subdued performance from the man who had been so influential in United’s revival under Solskjaer.
But Solskjaer claimed Pogba did not deserve to get a second booking for his challenge on Dani Alves.
“Paul is trying to get his body across and Dani Alves is clever enough to put his foot in there. Paul wants to shield the ball, he’s unlucky,” he said.
United’s cause was not helped by injuries to Jesse Lingard and Anthony Martial and Solskjaer admitted the loss of that duo’s pace was a blow.
“We had quality players to come on but Lingard and Martial give us something and let’s hope they are not too serious,” he said.
“They are muscle injuries, we have to wait a couple of days.”
United now face a huge task to reach the quarter-finals and Solskjaer called on his stars to produce a vastly improved display in the French capital.
“Mountains are there to be climbed, aren’t they? You can’t lay down and say this is over,” he said.
“We will go there, play our game and improve from today.”