The Reds host Sky Bet League One side Notts County in the second round of the competition and Rodgers is likely to make changes as he prepares for Sunday's league clash with arch-rivals Manchester United.
Yet he still sees the League Cup - of which Liverpool are record eight-times winners - as an important part of the season.
Rodgers said: "The league is the number one priority but this is a club with a tradition that is based on cup competitions and trophies.
"We're better equipped now this year, everyone is in tune with what we're trying to do on the field.
"I made some mistakes last season in terms of changing the team.
"The group is more prepared in every way this time around than what we were last year.
"The cup competitions are important, as well as our league campaign this year. We'll be giving absolutely everything to get as far as we can."
Liverpool will be expected to brush aside the Magpies, who have not won any of their opening four matches in League One, in the second-round tie at Anfield.
Rodgers said: "Our focus is, we are concentrating only on the next game and for us it is Notts County.
"We will treat them with the same respect as we will Manchester United.
"It will be an opportunity for some players, who maybe haven't featured, to get a game.
"But the core of our team will very much be there. We will have a strong side out."
Rodgers' own side have started well, securing 1-0 wins over Stoke and Aston Villa in their opening two games courtesy of fine Daniel Sturridge goals.
There may now be a temptation to rest Sturridge with the weekend in mind with Italian Fabio Borini hoping for a chance to impress.
The 22-year-old, who joined the club in a £10.5million deal last year, is still to establish himself at Anfield after a first season ravaged by injury.
Rodgers said: "Fabio will be in the squad. He's working very hard to come into the team and make an impact.
"For any player coming in here it takes a bit of time to adapt.
"There's no doubt he had a disruptive season last season with his injury and one or two other things that he would have wanted to be better.
"But Fabio is a worker and a grafter, a good kid who wants to do really well."
With Sturridge in form, new signing Iago Aspas looking to make his mark and the suspended Luis Suarez still to return, Borini faces stiff competition for a place.
But Rodgers hopes to keep them all firing and has had no thoughts of allowing Borini out on loan.
He said: "There would be a queue of clubs wanting to take him if he was available.
"But we want to keep a strong group, it's a very long season for us."
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