Villa are only three points above the bottom three after being beaten 2-1 at home by fellow strugglers Bolton on Tuesday night. Supporters called for McLeish to be sacked during the later stages of the game but Warnock believes it is unfair for the Scot to shoulder the blame.
Warnock said: "It's a natural reaction in football. The fans come, they pay their money, they are entitled to their opinion... The manager gets the brunt of the stick but it's down to his players on the pitch. If they don't perform or make errors, it's nothing to do with the manager."
He added: "It's down to us to go out and perform. It's our mistakes which have cost us at the end of the day, not the manager. The manager doesn't go to clear the ball and make a foul and that's down to our own individual errors and we need to learn from that.
"He can't legislate for someone making an error. That is part of the game but we've got to cut those errors out."
Warnock, on target against Bolton in his new midfield role, remains confident Villa will survive the drop.
He said: "It was a crazy two minutes that cost us against Bolton and it's something we were all very bitterly disappointed about in the changing room afterwards.
"We've got three more games left. It's not like it is the last day of the season and that defeat against Bolton has sent us down. We're in this and we're going to fight for it. We are still one game (win) away from staying up and I'm confident we will get it.
"Get a couple of lads back fit like Gabby (Agbonlahor), running at players, and we know we've got the players to cause problems. Personally I feel we are not far off battering a team."
But Warnock knows Villa's inability to kill off matches when in the driving seat is a key factor in their current predicament. He said: "The disappointing thing is we have conceded the most points in the Premier League from winning positions. That says something about the team. We've got to understand why we are doing that."