United, who won ten and drew the other of Solksjaer's first 11 matches, went behind in the 53rd minute when they switched off as Di Maria whipped in a corner for Presnel Kimpembe to steal in at the far post and smack home an unstoppable volley.
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.
And they will be without influential midfielder Paul Pogba in Paris on March 6 as the France global was dismissed in the closing stages, referee Daniele Orsato showing him a second yellow card after a foul on Dani Alves.
Kimpembe, who scored his first senior goal in Manchester, admitted that it was a dream-like scenario for him - even if he was fortunate to escape a second yellow card in the first half. But today is a reality check.
The home side never recovered their composure as PSG produced a stunning second-half display to all but book their place in the last eight despite David de Gea's best efforts.
"The second goal was quality by them".
"I know Paul wants to just shield the ball so he's unlucky that he hits (Alves) on the knee", Solskjaer said.
"You can see we haven't played games at this level for a while", Solskjaer said.
"I can't do anything about Alexis Sanchez", said Solskjaer. His speed is enough to take on an entire backfield, as we saw here, and he gave PSG a commanding lead in one of the more intriguing UCL knockout matchups.
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.
"It's not going to be a season defining one, it's one we have to learn from". A repeat of that 3-0 win in Paris next month would take United through to the quarterfinals.