Rodgers masterminded an unlikely tilt at the title last season, but the Merseyside club eventually had to settle for second behind Manchester City.
Prolific striker Luis Suarez left to join Barcelona in a big-money move last month, but Rodgers has bolstered his squad by bringing in a plethora of new faces as he strives to build on an impressive 2013-14.
Adam Lallana, Rickie Lambert and Dejan Lovren are among Liverpool's new recruits after they were lured to Merseyside from Sunday's opponents Southampton.
Rodgers believes his side can make their presence felt again in the Premier League title race, but stated that another top-four finish is his primary aim.
"What happened last season counts for nothing, but we carry the belief. We want to be competitive. [To] finish in the top four is our objective," he said on Friday.
"In the league it is about sustaining Champions League football.
"I've seen some odds and we're not even in the top four. People will rightly look to (Manchester) City and Chelsea, but we are here to challenge."
Even though Southampton have lost several of their leading players this close-season, as well as manager Mauricio Pochettino, Rodgers believes the south-coast club can perform well under new boss Ronald Koeman.
"Every club loses players, but they will hope they have the objectives to continue improving," he added.
England midfielder Lallana will play no part against his former club due to a knee injury, while fellow new boy Lazar Markovic (ankle) is also sidelined along with defenders Jon Flanagan (knee) and Daniel Agger (calf).
Striker Lambert and centre-back Lovren are in contention to make their Premier League debuts for Rodgers' side against their previous employers.
Lovren scored the only goal of the game at Anfield as Southampton consigned Liverpool to one of only two top-flight home defeats in 2013-14, although the Merseyside outfit got revenge by winning 3-0 at St Mary's Stadium in March.
Koeman has brought seven players in to his new club, and while he is anticipating a stern test at Anfield, he has warned Rodgers' team not to take Southampton lightly.
"We know it's a tough game but everyone starts on nil and everyone has to show qualities and I believe we are very well prepared to play," said the Dutchman.
"I know what it is to win at Anfield and they will have to play well to beat us."
The likes of Dusan Tadic, Shane Long, Fraser Forster and Ryan Bertrand are in contention to make their Southampton debuts this weekend, but Jay Rodriguez (knee) remains sidelined.
