United was forced to adapt, too, after losing Jesse Lingard and Anthony Martial to injury for the second half.
PSG handed United their biggest home defeat in Europe after Ángel Di María set up goals for Presnel Kimpembe and the hugely impressive Kylian Mbappé.
The English giants will also have to cope without Paul Pogba in three weeks' time as he was sent off for two yellow cards a minute from time to round off a awful night for the hosts.
The game could have finished 0-0 if they hadn't scored from that corner, but they did. He obviously hates YOUR football team and has no interest in synchronised swimming.
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.
"Today we weren't at the level, this is a level up from what we have played against".
"I can't do anything about Alexis Sanchez", Solskjaer said.
Fans will be waiting with bated breath for a diagnosis on both as United face a trip to Chelsea in the FA Cup on Monday, before tough Premier League games including rivals Liverpool's trip to Old Trafford, all ahead of the second leg.
The World Cup victor has scored eight goals and set up another five since Solskjaer took over in mid-December and having been given licence to roam from midfield has looked a player re-born.
None of the previous 34 teams to lose the first leg of a Champions League knockout match at home by two or more goals have progressed to the next round.
"You can see that we've not played games at this level for a while and we'll have to learn from this experience, because it was one of those experiences that can go either way".
Angel di Maria was roundly booed by the home support on his return to Old Trafford after an unhappy one-season spell with United after signing for a then club record £60 million in 2014.