Liverpool failed to fire in cup competitions last season, crashing out in the fourth round in both domestic cups, while also finishing seventh in the Premier League.
Rodgers has led Liverpool to wins in their opening two league fixtures and they face Manchester United on Sunday, leading to suggestions wholesale changes could be made to keep the squad fresh.
|5/1||Philippe Coutinho is 5/1 with Paddy Power to open the scoring against Notts County
"We will treat Notts County with the same respect as United. We want to do well in the cup competitions this year," he said.
"We will always respect whatever opponent we play, no matter what division they are in. Our focus is on ourselves to get the job done and get in the next round.
"The core of our team will be there. If there is an opportunity to recover one or two players who have niggles, then we will look at that – but we will have a strong side out.
"It’s very much at the forefront of our minds to go for silverware.
"I made some mistakes last season in terms of changing the team. The league is the No1 priority but this is a club based around cup competitions and trophies."