That feeling lasted until the French champions began to get a grip on the game and by the end of the night, a 2-0 defeat in the last 16, first-leg clash served to highlight the gulf that remains between this United team and the European elite.
Solskjaer was unfortunate to lose Martial and Lingard to muscular injuries before the start of the second half, and their withdrawals not only critically diminished United's ability to pin PSG back and defend from the front, but also served to highlight the squad's lack of depth.
It is painfully ironic that the very tactic of counterattacking which was linked to be the home-side's go-to measure turned out to be their bane.
"We have character, because it's not easy to play here, Man United are one of the best teams in the world".
Di Maria was the architect of PSG's victory, providing the corner that allowed Kimpembe to open the scoring in the 53rd minute before teeing up Mbappe on the hour.
Di Maria rose to the occasion amid the jeers to superbly provide assists for Presnel Kimpembe and Kylian Mbappe in a comfortable 2-0 first-leg win for the visitors. We have to bounce back, we're in a tournament and the Champions League is always going to be hard.
Solskjaer insisted his United side must treat their chastening defeat as a learning experience and demanded a response ahead of Monday's FA Cup fifth round trip to Chelsea and their following Premier League game at home to title challengers Liverpool. "Today was a kind of reality check on the level of these teams".
Ole Gunnar Solskjaer had won 10 of 11 matches since taking over from Jose Mourinho to restore confidence at United, but their loss to Les Parisiens served as a reminder of the progress they must make. "It's not going to be a season-defining one for us". "He needs to find himself when he plays because we know there's a quality player there".
Solskajaer said: 'You could see we have not played at this level for a while.
"The reaction in dressing room is disappointment but when we go to Paris we'll give it a go", he said. "We're Man United, we always bounce back".
While a two-goal lead is one of the flimsiest scorelines to carry forward given the dramatic history of the Champions League and Manchester United's tendency for comebacks, this one has an added element. That's the level we need to aim for at this club.
"Let me put it in another way, will Manchester United miss [Paul] Pogba if he was not there tomorrow, or [Marcus] Rashford?" he said.