It was a frustrating night for Solskjaer, who saw United suffer a third defeat in their last four games - underlining how much work the Norwegian still has in front of him following his appointment as permanent manager last week.
But Diogo Jota levelled after Fred gave away possession and United captain Ashley Young was sent off after being booked twice for fouls on the Wolves striker to become the 100th dismissal of Mike Dean's Premier League career.
The defeat has dealt a blow to United's hopes of securing Champions League football next season.
Smalling put into his own net from close range with 13 minutes left to win it for Wolves, who sit seventh in the league ahead of Sunday's FA Cup semi-final against Watford.
There was the game, there was a game plan, we take the decisions and the options and we prepare for the next one. We played so well in the first half an hour and we didn't quite react as well to their goal as we normally would do.
"So when you go back into the dressing room and say, "well done we played well and should have won because of the chances we created", then that would just make me think we didn't play well".
The youngster was fantastic in midfield for Ole Gunnar Solskjaer's men, even opening the scoring which was essentially his first goal for the club.
"[It was] one of those days that we have done more than enough to score two or three goals".
But with Wolves' defence looking curiously disorganised, there was still opportunity for Lukaku to chip in a unsafe centre for Lingard, whose close-range header was pawed away to safety by Patricio. But the game turned on right back Young's sending off for a second yellow card after a reckless hack on Jota.
"I was very pleased with the intent, the way we started".
"Good performance, in the beginning they started better and controlled the game", Nuno said. "It made it more hard".
There's little doubt that McTominay isn't going to be the player to grab the headlines for Manchester United, especially with the next batch of players in the academy looking so impressive.