Lambert's job at Villa Park came under fire again on Tuesday as the Premier League strugglers were knocked out of the Capital One Cup semi-finals by League Two side Bradford City.
Vlaar said: "The players are still all behind the manager. That is not an issue. Why should it be?
"I believe he is the right man for the job. We have to pick ourselves up. We have no option."
Villa are currently one point above the relegation zone in the Premier League table.