Former manager Sir Alex Ferguson was in attendance at Old Trafford for the first time since suffering a brain haemorrhage in May and United were unable to secure a win.
Although Fred gave the hosts the lead against the run of play in the 18th minute , Wolves battled back and deservedly levelled just after the break – Joao Moutinho finding the top-left corner after good hold-up play by Raul Jimenez.
United piled the pressure on towards the end, though clear-cut opportunities remained infrequent and Wolves held on to a well-earned point.
"Everyone is disappointed," the Belgian told Premier League Productions. "We know we can do better.
"We had to win today because after that it will be difficult to close the gap. Everyone is disappointed, but that is football.
"We have to move the ball quicker, when we create the chances we have to score."
And a frustrated Jose Mourinho was scathing in his assessment of his team for how they got caught on the ball in the build-up to Wolves' equalising goal.
"It’s a situation that the players knew perfectly, that they press in midfield," he said after the game.
"These two Portuguese boys [Ruben Neves and Moutinho], they are both the kind of player that likes to bite, that likes to [give] short distance, to press, we know that they don’t give a long time for you to have the ball, to turn, to one-touch, two touches.
"You don’t have much of that, so you concede in a situation which is much harder to accept but that is one goal that you concede and you have 90 minutes to show a different attitude and I think we have to do better."