The Red Devils took the lead through Fred in the first half, but they were pegged back in the 53rd minute when Joao Moutinho hit an equaliser for the visitors.
The result continues Manchester United’s stuttering start to the season in the Premier League.
Jose Mourinho’s men have only won three of their opening six Premier League games and find themselves eight points off the top spot.
It has left the Red Devils with a serious mountain to climb if they are to claw their way back into contention in the Premier League title race.
And former Liverpool FC star Murphy has admitted that Manchester United are struggling to dominate teams in front of their home fans at Old Trafford.
Speaking on Match of the Day on Saturday night, Murphy said: “Teams are now going to Old Trafford without that fear factor
“Wolves deserve huge credit. There has been a lot of talk about energy and tenacity but the quality on the ball are a real threat.
“They’ve had a lot of shots and we know that because of the numbers but they haven’t scored a lot. They’ve only scored six goals all season.
“But Costa, Jimenez and Jota will score more goals with a bit more care in the final third. They caused United all sorts of problems.
“What I like about them is they defended really well but when they went forward, all the time they were trying to bust a gut and get into the box.
“The manager is right. As the game wore on, with a little bit more calmness, they could have beaten United.”
Manchester United will now switch their focus to League Cup affairs and their home clash against Derby County in the third round on Tuesday night.
The Red Devils are aiming to challenge for the Premier League title this season after they finished second and without a trophy under Mourinho last term.
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