Fred opened the scoring after 18 minutes, with a goal that owed everything to a selfless and clever assist from team-mate Paul Pogba.
But Mourinho was again left questioning the attitude of his players after what was a thoroughly deserved point for Wolves, who could have left with all three.
Martial scored in United's 3-0 win over Young Boys in the Champions League on Wednesday, but the France global will have to settle for a place on the bench against Wolves.
United manager Jose Mourinho had boasted of his team's defensive improvements following a strong start to September in which his side had won all three of their games in the league and Europe.
The draw keeps Wolves one point behind Manchester United in 10th, as Mourinho's side climb to fifth.
This will lift his confidence and help him play more freely.
David de Gea came to United's rescue after seven minutes, as he produced a superb save to deny Raul Jimenez from 10-yards out.
The rumours have only been heightened following reports from The Mirror that the Spanish giants plan to watch every game the Frenchman plays from now until the end of the season, before launching a bid for the World Cup star next summer.
"I think the happiness, the confidence, the self-esteem was what pushed him to play the first match nearly without training against Leicester and played a very good match".
"I think good results, and good performances, they make miracles", said Mourinho at his press conference on Friday. We come home with a good spirit, we come home let's say in peace because we recover.
"So he played 90 minutes in the Champions League on a hard pitch, recovered totally and on Tuesday he plays again. But I think we are going to be a better team".
"So, they got this season, the Portuguese national team goalkeeper [Rui Patricio], they got [Joao] Moutinho, who is one of the players of the 100 caps club".
"I'm proud of the way we started the game, and proud of the character we showed after, when we were (1-0 down)", he said.
In a match where United needed some creative spark, instead of lumping the ball forward looking for Marouane Fellaini for the last 20 minutes of the match, Alexis Sanchez was very much needed. "They did. That attitude made a difference", added the former Chelsea manager.
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