Asked whether his side were contenders to be English champions in 2014/15, Rodgers replied: "Not according to the bookies we're not.
"I've seen some odds and I don't think we are even in the top four. I think people will look at Manchester City and Chelsea, with their squads.
"We probably arrived a year early to where we were but we will look to be up there challenging again this season.
"What happened last year counts for nothing, that's all gone now. The one thing that will carry on from that is the belief.
"Our aim is to be competitive. Like the top teams, we want to win a trophy. That would be an aim. In the league, it's about sustaining Champions League football.
"For that you want to arrive in fourth. Once you have consolidated that, you can look beyond that. That's certainly our aim this season."
And Rodgers believes teenage forward Raheem Sterling will just get better and better.
The 19-year-old was a member of England’s World Cup squad in Brazil and Rodgers added: "He is a wonderful talent. He is very stable and secure outside of his football life and you see the joy he plays the game with.
"The great thing about Raheem is he has a real mature head on his shoulders.
"He got 10 goals last year and we are looking at improving that ratio.
"He is one of a number of youngsters here who has so much potential to produce."