Saturday's 1-0 loss at Crystal Palace left Villa four points above the relegation places - just four weeks after victory over Chelsea took them into the top half.
Anti-Lambert chants were clearly audible among the away supporters at Selhurst Park, and Paul Faulkner has issued a statement appealing for unity ahead of what is now a fight for Premier League survival.
It read: "We have suffered four consecutive defeats and that is hard to take. We are hurting. Fans are hurting, players and the manager are hurting. The frustration is shared by everyone who loves Aston Villa.
"Now more than ever it's time for us all to pull together - fans, players, the manager, everyone at the club.
"Our immediate focus and combined efforts need to be concentrated on our game against Southampton this weekend and on our remaining games of the season.
"We know we can handle adversity. What we need now is for everyone to stick behind the team and continue to show the great support that is a hallmark of our club."
Faulkner's call has been echoed by Lambert, who must now regroup for a five-game run-in that finished with trips to Manchester City and Tottenham.
"Now it's about stopping the run," he said. "We have to win a game of football. You don't shy away from it. You have to meet it. You have to stop that sequence of losing.
"The lads never ever give up. They might get beat but they never give up. They give me absolutely everything. I don't waver for one minute in my belief in them.
"We will need the crowd behind us too. We have a fantastic fanbase. They are vital, absolutely vital. They will roar us from now until the end of the season. Since I have been, the Villa fans have been excellent."