Scott McTominay put Solskjaer’s side in front after 13 minutes before Romelu Lukaku and Jesse Lingard both wasted good chances to double the lead.
Diogo Jota made them pay after 25 minutes and the visitors were reduced to 10 men when Ashley Young was shown a second yellow card before Chris Smalling turned into his own net on 77 minutes to compound United’s misery.
Solskjaer insisted he was happy with the overall performance and singled out McTominay for praise after watching his all-action display in midfield.
But the Norwegian was left frustrated by a failure to take their chances as his side fell to a third defeat in their last four games to leave them trailing in the race for the top four.
“I think we played some fantastic stuff, first 20 minutes we should have been two or three up and I’m not exaggerating,” he said. “We didn’t pounce on big moments in the game.
“Scott McTominay played really well tonight, he’s been excellent. He gave us a goal threat, energy and legs – very pleased with him.
“There’s a couple of mistakes from us. We gave them that first goal, we have to be honest.”
Solskjaer conceded that Young deserved to be sent off after he was booked twice within the space of five minutes for fouls on Jota.
“When you’re on a yellow and you go in you’re always in danger of getting another one,” he added.
“He hit the ball but followed through and hit him. It’s a yellow card.
“At 10 men it’s hard but we had to keep the ball. We didn’t want them to put pressure on us.
“They scored with their first chance after the sending off and you have to give them credit for that.
“Very disappointed with the result but pleased with the performance up until 75 mins. An excellent performance from the boys.”
The result leaves United fifth in the Premier League table, level on points with fourth-placed Tottenham who have a game in hand are currently ahead of United on goal difference.
Third-placed Arsenal have also played one fewer game and are two points ahead of United.
Meanwhile, Wolves cemented their place in seventh in the table and are on course for their best top-flight finish since 1980.
Attention for Nuno Espirito Santo’s side now turns to their FA Cup semi-final clash with Watford on Sunday and the manager was delighted with his players after an impressive victory.
“Tonight was a good night, a good game of football,” he said.
“What more can you ask? We know it was very difficult. The extra effort the boys make and they then react to the first goal – I’m really pleased.
“I give credit to United for how they shaped themselves, it was difficult to recover the ball. The way we reacted was amazing.
“Even after the red card it is always difficult against United. We created spaces and had more chances. If there’s one thing I can complain about it is being more clinical.
“The preparation starts now for the semi-final – we will rest and prepare for a difficult game. A fantastic challenge for us.”
Manchester United’s remaining Premier League games
Apr 13 West Ham (h)
Apr 21 Everton (a)
Apr 24 Manchester City (h)
Apr 28 Chelsea (h)
May 4 Huddersfield (a)
May 12 (Cardiff (h)
Wolves’ remaining Premier League games
Apr 13 Southampton (a)
Apr 20 Brighton (h)
Apr 24 Arsenal (h)
Apr 27 Watford (a)
May 4 Fulham (h)
May 12 Liverpool (a)