Barring an incredible comeback in the French capital in three weeks' time, United will miss out on the Champions League quarterfinals for the fifth straight year, AFP reported.
Even with the injury-enforced absences of the world's most expensive player Neymar and the prolific Edison Cavani, PSG was simply too good for Solskjaer's men, with the 2-0 scoreline at Old Trafford on Tuesday only kept respectable by United goalkeeper David de Gea's efforts in the second half.
"This is a level up from what we've played against with the games we've had," admitted Solskjaer.
The man who scored the winning goal when United won the Champions League in 1999 had won 10 and drawn one of his first 11 games in charge to lead United back into the top four of the Premier League – the passport into next season's Champions League.
But as a player under Sir Alex Ferguson, Solskjaer was used to regularly being in contention to win the competition, not just taking part.
"There is a reason for them being one of the favorites for the Champions League. Then again, that is the level we need to aim for at this club," the Norwegian said.
"We've been talking about top four. Top four is one thing but we want to be at the top.
"Man United should be at the top and this is a top, top team we are playing against. Our players today are disappointed after the game of course, but I also think they know we need to step up our level to get to the level we want to get to."
The reality of where United stands among the European elite did not just bite on Tuesday – the defeat was further evidence of its struggles since it reached a third Champions League final in four years in 2011.
In the past eight years, United has won just one knockout match in the Champions League – at home to Olympiakos during David Moyes's short-lived tenure in 2013.
"You can see that we've not played games at this level for a while and we'll have to learn from this experience," said Solskjaer. "It's not going to be a season-defining one for us. It has to be one that we're going to learn from."
"We are looking to strengthen the squad then again we have to learn with so many young players that we have, to make the step up next season."
How much of a blow failure to progress is to Solskjaer's chances of being in charge next season on a permanent basis remains to be seen.
But the lack of a response to losing Anthony Martial and Jesse Lingard in quick succession to injury toward the end of the first half underlined why planning on overhauling the squad needs to start straight away.
Juan Mata and Alexis Sanchez made little impact off the bench, with the Chilean's anonymous display again raising doubts over his future after a return of just five goals in more than a year since joining from Arsenal.
"I can't do anything about Alexis Sanchez," Solskjaer said. "When he plays he needs to find himself because we know there is a quality player there."
'Stop scare stories'
Mbappe called for an end to the "scare stories" about injuries to players Neymar and Cavani after the victory at Manchester United.
"We need to stop with the scare stories. People need to stop being afraid," the 20-year-old striker said, BBC Sport reported.
"We showed that tonight. We're good."
Mbappe is the club's top scorer, with his goal against United his 23rd of the season in all competitions. His 14th Champions League goal means he has already drawn level with France great Zinedine Zidane.
"Of course Neymar is hugely important and Cavani is fundamental to us, but football is played on the pitch and we showed that today," he said.