Villa are still hovering just above the Barclays Premier League relegation zone despite earning a valuable point at Chelsea from a 3-3 draw on Sunday.
Houllier has come under fire from some supporters after replacing Martin O'Neill, who quit five days before the start of the new campaign.
But Faulkner, Villa owner Randy Lerner's right-hand man, is adamant the belief in Houllier has not wavered.
Faulkner said: "I believe in what we are doing. This is a great club. We know we are going to have periods of adversity when things don't go our way.
"But, if you are well run, you will come through those and emerge better and stronger."
Source: PA
Source: PA