Questions have been raised over the future of the former Birmingham City boss as the supporters become increasingly frustrated with the 53-year-old.
"I can understand the fans' reaction," said McLeish. "We went into a deserved lead [against Bolton] and to see the game turn like it did was horrible. The reaction was a first for me. But, like I said, it was understandable because we had the three points in our grasp.
"I spoke with Randy [Lerner] and Paul Faulkner after the game and they were supportive and said to keep your head up. They said everyone has to stay together and battle through this fight."
Villa have three games left to secure Premier League survival.