The French heavyweights were shorn of Edinson Cavani and Neymar for the first leg of this Champions League last 16 tie but still proved too strong for United as Presnel Kimpembe and Kylian Mbappe secured a 2-0 win at Old Trafford.
A loss for the Red Devils was compounded by the late dismissal of Paul Pogba, who will miss the second leg at the Parc des Princes, and Solskjaer lamented a gulf in class between the sides.
Nevertheless, Solskajer, who presided over 10 wins and a draw in his first 11 fixtures, insisted United must learn from such setbacks if they are aspiring once again to be among the cream of the European elite.
He said: "We weren't at the level. This is a level up from what we have played against with the games we've had.
"We've had a great run, we came into this game in a great frame of mind, great form, but of course it was a big step up, they have quality from the keeper to the striker.
"There is a reason behind them being one of the favourites for the Champions League. That's the level we need to aim for at this club.
"Of course it's a reality check. The top four is one thing but we want to be at the top and Manchester United should be at the top.
"This is a top, top team that we played against. Our players are disappointed after the game, of course, but I also think they know that we need to step up our level to get to the level that we want to get to."