Roger Johnson gave Blues the lead early in the second period but a deflected shot from Villa centre-back James Collins ensured the game ended all square.
McLeish felt that Blues had enough clear-cut opportunities when in front to wrap up the game in addition to having yet another penalty claim rejected, this time by referee Mark Clattenburg.
The Blues said after the game: "It was probably a fair result overall.
"We have come a long way in a couple of years in terms of these derby games and the results. Had we been a bit more clinical at 1-0, we would have seen it through.
"Craig Gardner had a wonderful chance with a volley which he put wide and he is a guy you would normally want and trust in that situation. Brad Friedel also made a great save at that point from Matt Derbyshire and we had the chance to turn the screw.
"But we allowed Villa to come back into it, and gave away a few unnecessary free-kicks and I was disappointed with the build-up to their equaliser.
The shot from Collins was not even on target before it hit Liam Ridgewell and was deflected in."