Houllier said: "We're struggling at the moment but we're grateful to the fans because even when Emile Heskey was going through a bad patch they chanted his name and supported him.
"The boys appreciate that because it is a time when we need to stick together. It is a challenge, but we showed we had character.
Houllier added that he still has complete faith in the squad that he has carefully assembled during his tenure as Liverpool manager.
"I said to the boys at the end of the game, I care about you. I trust you. We are in this together. You don't have to feel guilty. If we stick together it will come and the reward will be greater."