Villa took the lead with a stunning effort from Andreas Weimann but Stoke fought back and were rewarded with a header from Robert Huth and could easily have gone on to win the game.
But McLeish, who is obviously out of his depth with a club like Villa just moaned that Huth had won the header unfairly.
The Scot argued Stoke goalscorer Huth impeded James Collins before netting the equaliser.
He said: "I am disappointed we didn't get a second goal to put it beyond Stoke because they are always going to threaten you at the set pieces.
"The big disappointment was that I felt the goal should have been disallowed because Huth had his hands on James Collins shoulders and he couldn't get off the ground regardless of whether Huth was up in the air or not.
"I also felt that that free kick leading up to the goal was one of the softest I have seen this season, our man concentrated on the ball and kept his arms at his side and (Jermaine) Pennant eased in front of him and used his experience to get the foul."