The Anfield club had been in a strong position last season, only for their championship bid to founder on a defeat by Chelsea and the surrender of a three-goal lead against Crystal Palace.
Liverpool have also lost top scorer Louis Suarez this summer, albeit the club have enjoyed a productive transfer window by signing such as Adam Lallana and Dejan Lovren. Both players were recruited from Southampton - a team which visits Anfield on the opening day of the campaign.
Rodgers is optimistic that the league trophy will also be on show at the stadium come May. "I wasn't lying on a sun lounger over the summer crying over the fact that we lost the league last season," he said. "There is only an excitement and a belief that we can challenge again for the title this time. We must believe that we can go one better."