United missed the chance to book their place in the Champions League knockout stages after suffering a 3-1 defeat to PSG at Old Trafford on Wednesday night.
Neymar volleyed the visitors into a sixth-minute lead in Manchester, and they almost added to their tally moments later when Alessandro Florenzi's fierce shot was parried away by David de Gea.
The Red Devils were lucky not to be reduced to 10 men 20 minutes into the contest, as Fred escaped a red card after pushing his head against Leandro Paredes, with the referee only handing out a yellow to the Brazilian after checking his VAR monitor pitchside.
Solskjaer then saw his side draw level on the half-hour mark when Marcus Rashford's deflected effort trickled into the net after deceiving PSG goalkeeper Keylor Navas, setting up an enthralling second half.
Anthony Martial should have put United into the lead minutes after the restart when Rashford set him up in front of goal only for the Frenchman to blaze over the bar from five yards out.
Edinson Cavani came even closer to completing the turnaround when his delightful chip over Navas bounced back off the bar, before PSG made the hosts pay for their wasteful finishing.
Neymar whipped in a corner in the 68th minute which caused havoc in the Red Devils penalty area, and Marquinhos managed to capitalise on the chaos by turning the ball past De Gea from close range.
Fred then picked up a second yellow card for a rash tackle on Ander Herrera, leaving his team with a mountain to climb in the final twenty minutes.
United pushed hard for a crucial second goal but ended up being caught on the break in stoppage time, with Neymar tapping home his second of the game to wrap up the victory for Thomas Tuchel's men.
Owen thinks Fred should be dropped for his ill-discipline, but also admits that Solskjaer deserves to take a share of the blame after failing to use one of his five substitutions to take 27-year old out of the firing line.
"Mistakes all round really," the ex-United striker told BT Sport .
"It [the clash with Paredes] was a red card. You’re a grown man, you don’t need to do a petulant thing like that to put your team at risk.
"If I was a manager, and one of my players did that, he would never play for me again. It’s pathetic. Overall you have to blame Fred but also Solskjaer.
"The manager has to protect him and the team in that situation so they’re both to blame."
PSG are now favourites to qualify from Group H as they look ahead to a home fixture against Istanbul Basaksehir on matchday six, while United will travel to RB Leipzig knowing a defeat will send them out of Europe.
"PSG are going to go through so basically it’s a shootout between Manchester United and RB Leipzig," Owen added.
"Both teams can score but both teams look vulnerable. United should not go there with any fear.
"I think they will score goals in Germany so I still fancy Manchester United to get a draw or a win but they’ve made it dangerous for themselves."