Rodgers was brought into Liverpool to replace club icon Kenny Dalglish after the Reds finished a disappointing eighth in the Premier League.
Dalglish did win the Carling Cup last season and reached the FA Cup final, but failed to deliver a top four finish and a sought-after return to the UEFA Champions League.
Rodgers is confident Liverpool can recapture former glories, but insists he needs time to transform the club's fortunes.
"We have to recognise the challenge is immense, let's be under no illusion," said Rodgers.
"But I certainly think that a club of our status and value to the football world can go again.
"It's going to take time. And whether it will be in my time, I'm not so sure. But I'm going to fight for my life to try to get this model of play that, hopefully, can change the history of the club.
"This is a club where trophies are what it has been about for many years. But, for me, running alongside that it's about putting in place a model to see the club grow. That is equally important. To build a group that challenges."