The Villains started slowly in west London, before Barry Bannan gave the midlands outfut a lead from the penalty spot in the second-half. However, an unfortunate Richard Dunne own goal in injury-time meant the points were shared.
It was a disappointing end for the visitors after finding themselves in-front, but McLeish is eager to fix the problems that saw his side on the back foot for the opening period.
"The Villa fans supported us magnificently today - I'm gutted for them and also the team because they played so well second-half," the Scot told Aston Villa TV.
"First-half I don't know why we didn't turn up, we had to defend it really well to stay at 0-0. We never threatened at all up-front.
"Second-half was better but I've got to find out why we started as poorly as we did."
On the first-half, McLeish was happy to see his side show some resilience defence, the only positive in a period dominated by the Hoops.
However, the opportunity to claim three points was not lost on the former Birmingham boss, who felt his forwards could have taken more care in securing victory.
"That is the one thing that you have to applaud them for. The players dug in when we were under pressure and we didn't really look like we would lose a goal, but you see what happens with two minutes to go.
"Just a punt up the pitch, are two centre halves - who were immaculate - end up being in there, and that's what happens. If centre halves make mistakes it results in a goal-scoring opportunity.
"I really feel for Dunney and James (Collins) that we should lose that but we had opportunities in the second-half. If we'd taken care in the final third then we could have had more goals and that would have put QPR away."