Despite the club going through their worst run of form in 22 years, Houllier insists Benitez is the right man in charge.
The former Reds manager told the Sunday Express: "The sabbatical I had after leaving Liverpool helped me. I did only TV work in France for a year and then went to Lyon and won two championships.
"But I am proud of my time at Liverpool. The reaction of the fans was special for me the other night. I was extremely moved. I always tried to do my best for them and I think they realised this. I saw Rafa before and after the game. We don't know each other that well, but we respect one another. He seemed okay. He wasn't too down. He understands the situation.
"It will come good. Why? Because it is a big club, a big team and a good staff. I am sure of that.
"Liverpool are depleted by injuries at the moment. I see their games regularly on French television and it was not the same team against Lyon, but a draw would have been a fair result.
"In the big games you need your big players. Liverpool didn't have Steven [Gerrard], Torres and Johnson.
"The team is going through a bad patch. It happens and you are only one game away from a crisis in football today.
"It happens to all the clubs. It will be another team soon because when the injured players are back they will start winning again."