Supporters called for McLeish, who went down with Birmingham last season, to be sacked after Tuesday night's home defeat by Bolton and Lerner and Faulkner understand the frustration of supporters. But the duo have issued a rallying cry with Villa three points above the bottom three after registering only one win in their last 13 games.
Lerner and Faulkner, in a joint statement, said: "We will continue to support and rely on our manager and the squad and therefore give them our full support."
They added: "We are totally conscious, as is everyone at the club, that this is a very trying time for those who love Aston Villa.
"We know that the team will continue to fight through every minute of the remaining games and we hope Villa fans will continue to show their great support."
Villa have away trips to West Brom and Norwich sandwiched either side of the home clash with Tottenham.
The statement adds: "Right now everyone connected with Villa is hurting badly. We very openly acknowledge the frustrations of Villa fans and share in them completely.
"What matters to us and the board at this moment is how we, as a club, handle adversity and the pressure it brings. Our horizon is the next three games and we continue to be in control of our own destiny."
Villa midfielder Stephen Warnock insists the players - and not manager McLeish - should shoulder the blame for the club's slide towards relegation zone.
Warnock said: "The fans' reaction during the Bolton game is a natural reaction in football. The fans come, they pay their money, they are entitled to their opinion.