BBC Radio Merseyside. "He's starting a new cycle with the team.
"It will take a minimum of two years, maybe three, to achieve success. If the owners are patient, it will come good."
Liverpool are 12th in the Premier League, having taken 10 points from their first nine matches.
Houllier has described the 39-year-old from Northern Ireland as a "brave" manager and believes that quality will endear him to Liverpool supporters.
"I think he will [get time] because now the fans know that he wants to play a certain style that suits the team very well," added the Frenchman, who was manager of Liverpool between 1998 and 2004.
"He's also giving a chance to young players. There were three or four players below the age of 20 in a big derby. When experience comes along, they will get better and better.
"He doesn't look as if he lacks courage. Brendan is brave and he took some important decisions before the derby game with Everton [which ended in a 2-2 draw]."