The Scot has been targeted by fans over the course of this season with criticism worsening in recent weeks, as Tuesday's 2-1 defeat by Bolton left the side three points off the Barclays Premier League bottom three.
Supporters are planning further protests for Villa's home match against Tottenham on May 6, but ahead of Saturday's away clash at local rivals West Brom, McLeish said of the boo boys: "It's part of football and it's not something you can change. You have to accept it. If you don't want to hear that, don't be in this game."
He insisted his skin is thick enough to take the fans' stick, and has lamented the injuries and illnesses which have contributed to Villa's plight.
He said: "In terms of the abuse, there was nobody more disappointed after the Bolton game than me. I was absolutely gutted. I'm telling you, I don't care what any supporter says, there was nobody who felt as bad as I did going off that pitch.
"I don't criticise the fans for having a go or booing at the end of a game, when it's another home game we've lost and defeat was snatched from the jaws of victory, in what was a blooming good performance. We definitely deserved more but we didn't get it and it's left us with a battle for the next nine points."
McLeish refused to contemplate whether he would still be in charge at Villa Park next season. "I'm not thinking about my future, I'm concentrating on these nine points," he insisted.
Asked if he would leave if Villa did not stay up, he said: "I can't say, it's all hypothetical."
His stock is unlikely to rise with Villa fans even if he avoids relegation, but he believes he can still get supporters back on side.
"Well, let's see if I can turn it. I believe so. I've done it before. I've done it at Rangers. We had a bad year then turned it again with some good planning and that always helps."