Supporters chanted 'you're getting sacked in the morning' after Villa were beaten 1-0 at home by Sunderland which saw them slip into the bottom three of the Barclays Premier League.
A goal from former Villa loan signing Phil Bardsley meant the Midlands club slipped into 18th position in the table.
Houllier received words of encouragement from Faulkner after the final whistle and is adamant that Lerner also remains supportive.
The former Liverpool boss said: "I spoke to Paul Faulkner and he was very supportive.
"I don't doubt Randy Lerner's firm support and determination. We are in this together for better or worse."
Houllier admitted to being "hurt" by the fans' chants but also understood their frustration.
He said: "I understand the fans' frustration and the players can't complain about the fans because, when we were under the cosh, they were still supporting the team."
Houllier is also convinced that Villa will climb out of their current predicament.
He said: "We knew we had a difficult programme up until February but hopefully after that we will be better.
"It is very tight in the table and one win can move you up. All we need at the moment is to keep morale and confidence."
Houllier felt the sending off of striker Emile Heskey midway through the second half for violent conduct, when he pushed Jordan Henderson, was crucial.
He said: "There were two extremely crucial moments, when Emile missed a sitter and then was sent off.
"I have not seen it again but he put a hand in his face and the regulation is clear although it is harsh."
Sunderland manager Steve Bruce admits that victory came at a heavy price in terms of injury setbacks.
Bruce confirmed that midfielder David Meyler had suffered cruciate knee ligament damage and will be out of action for at least six months.
In addition on-loan Manchester United striker Danny Welbeck suffered a hamstring injury which will be scanned tomorrow.
Bruce believes the heavy festive programme is to blame for such setbacks.
He said: "In the Premier League you get players having to play five games in 13 days and players are picking up injuries through fatigue."
He also felt that the late sending off of Boudewijn Zenden for two bookable offences was "the softest red card you will ever see".
Bruce said: "It was a tremendous victory but I think we have now got 10 players missing and we may have to bring one or two bodies in during January."