McLeish believes that young winger Albrighton could have prevented the equalising goal.
"I'm disappointed we didn't hold on," the Scot told BBC Sport. "I had a good feeling we would.
"It's such a shame that Marc Albrighton tracked Victor Anichebe back but just didn't do the final thing to stop him. We are gutted by that.
"It's a good learning experience for him. It hurt us a wee bit by not getting the three points."
The result means that Villa have picked up five points from a possible 18.