McLeish revealed chairman Randy Lerner and chief executive Paul Faulkner had spoken to him after the final whistle.
He said: "They were supportive, they said 'you've got to keep your head up'.
"They said everyone has to stay together and battle together and see it through.
"It (the fans' reaction) has also not weakened my resolve to carry on and see this through. Absolutely not. I'm not someone who shirks a challenge and I'll keep going."