Villa suffered a shock 4-3 aggregate semi-final setback against npower League Two side Bradford despite winning the second leg 2-1 at Villa Park.
It was the latest blow in a season where the club have become embroiled in a Barclays Premier League relegation battle.
Bradford fans chanted `you're getting sacked in the morning' to Lambert during the second half.
But Vlaar and his team-mates retain total faith in Lambert whose position is not under threat.
The Dutch international said: "The players are still all behind the manager. That is not an issue. Why should it be? I didn't hear the Bradford fans sing that (about being sacked). I cannot believe that will happen.
"I believe he is the right man for the job."
Villa now face another tricky clash at Millwall in the FA Cup on Friday evening.
But Vlaar is aware the main priority is top flight survival ahead of next Tuesday's home meeting with fellow strugglers Newcastle.
He said: "We have to pick ourselves up. We have no option. We have no choice. We are fighting really hard in the league. Everyone is very disappointed. We have to get ourselves together and start over again.