The Midlands club are are only four points from safety and hang precariously close to the Premier League relegation zone with just two games remaining.
However, McLeish, who took over at Villa Park last summer, has full belief that the club can avoid the drop to the Championship.
"I have had to show my experience and leadership. I will not curl up and die," said the 53-year-old. "I will persevere to the end as I always have done.
"It gives me great pride to be manager of these players. We have had some troubles this season but we have some key players back now."
The Scot will now prepare his team to host Tottenham Hotspur next Sunday.