A 2-0 victory in the Champions League — consigning Solskjaer to the first loss 12 games under his caretaker command — was produced by PSG on Tuesday without two of the French club's fearsome forwards.
Neymar was already ruled out with a broken foot when Edinson Cavani hurt his left thigh at the weekend to join the world's most expensive player on PSG's injury list.
"They were a level above us," Solskjaer said after the first leg of the last-16 contest which saw United's record-signing Paul Pogba sent off.
Old Trafford instead became a stage for Kylian Mbappe to shine in tandem with Angel Di Maria, who relished the revenge mission on his return to his former club.
By the time Di Maria responded to the torrent of abuse by picking up a bottle of beer hurled at him and taking a sip, PSG was already leading thanks to academy graduate Presnel Kimpembe's first PSG goal in the 53rd minute.
Di Maria, who struggled in his only season at United before being offloaded to PSG in 2015, sent in the corner that Kimpembe raced into the penalty area unchecked to meet with a volley.
The second goal, on the hour, was the culmination of an electric counterattack. As Di Maria sent in a cross, Mbappe darted between center backs Eric Bailly and Victor Lindelof and clipped the ball under goalkeeper David de Gea for his 23rd goal of the season.
"It was a perfect pass for Kylian," PSG coach Thomas Tuchel said. "It was a nice comeback for him."
Less so, initially.
"In the first half it was a bit hard for him playing right in front of me and losing many easy balls," Tuchel said. "Maybe he was a bit nervous and a bit overused because he plays all the time for us. I'm happy he stayed confident. He's always super reliable."
Without two of its usual front three, the French league leaders commanded the midfield instead, with Marco Verratti often the orchestrator.
"It was a new system and we weren't really used to it," Mbappe said. "We had a lot of midfielders and not many forwards. We needed time to adapt."
United was forced to adapt, too, after losing Jesse Lingard and Anthony Martial to injury for the second half. Substitute Alexis Sanchez struggled to impose himself up front.
"I can't do anything about Alexis Sanchez," Solskjaer said. "When he plays, he needs to find himself because we know there's a quality player there."
Solskjaer is capable of transforming the fortunes of players — just look at Pogba.
United will be without its French playmaker in the second leg on March 6 in Paris after he received a second yellow card in the 89th minute for a lunge on Dani Alves.
"I know Paul wants to just shield the ball so he's unlucky that he hits (Alves) on the knee," Solskjaer said.
Not only was it a first loss for Solskjaer since replacing Jose Mourinho, but the heaviest-ever home defeat for United in Europe, having previously only been beaten by one-goal margins.
In the night's other last-16 game, teenager Nicolo Zaniolo scored twice to lead Roma to a 2-1 victory.
United's lackluster performance was a continuation of the European form under Mourinho in the group stage. United has only scored one goal at home in four Champions League games this season, a 1-0 victory over Young Boys.
"It was one of those experiences that can go either way," Solskjaer said. "It's not going to be a season-defining one for us. It has to be one that we are going to learn from."
Aside from victories in north London against Arsenal and Tottenham, facing PSG was United's biggest test since beating Italian champion Juventus at Turin in November in the group stage.
"You can see we haven't played games at this level for a while," Solskjaer said.
Twenty years after winning the Champions League as a United player, this was Solskjaer's first taste of the competition in management having only previously coached Molde in his native Norway and Cardiff before being hired by United.
Solskjaer was still Cardiff manager when United last won a knockout phase game in the Champions League — against Olympiakos under David Moyes in March 2014. A repeat of that 3-0 win in Paris next month would take United through to the quarterfinals.