The Red Devils were looking to return to winning ways following a 3-3 draw with Sheffield United in the Premier League last weekend.
However, the home side were behind in the 11th minute when Aston Villa captain Jack Grealish broke the deadlock with a superb curling shot.
Manchester United levelled in the 42nd minute after Tom Heaton’s own goal before Victor Lindelof edged the 20-time champions into a lead midway through the second half.
But Aston Villa left Old Trafford with a point thanks to Tyrone Mings’ equaliser two minutes after Lindelof’s goal to secure a 2-2 draw.
Manchester United are now in ninth place and 22 points adrift of Premier League leaders Liverpool FC after 14 games.
BBC Sport pundit Waddle didn’t hold back in his assessment of Manchester United’s performance.
“Villa have dominated the first half, but then Man United have upped the tempo and they have been better, but still not good enough,” Waddle told BBC Sport.
Waddle added that Aston Villa deserved to leave with three points after their impressive performance at Old Trafford.
“Manchester United have spells of 15 minutes when they move it well and there’s lot of energy and it looks good on the eye,” Waddle added.
“They are good when they play at high tempo and move the ball quickly but they seem to play at a slow pace and it does not suit them.
“Villa looked like the home side for a long period of this game.
“In the second half United upped the tempo but Villa lived with them and they deserved to win the game.”
Manchester United are in ninth place and eight points adrift of fourth-placed Chelsea FC.
The Red Devils will return to Premier League action on Wednesday night when Spurs make the trip to Old Trafford.
Their former manager Jose Mourinho will return to Manchester United for the first time since his sacking 12 months ago.
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