The Reds have suffered shock defeats in this competition in recent years, most notably to Northampton Town in 2010.
Rogers, whose side have won both of their opening Premier League fixtures, does not want history to repeat itself.
Liverpool face Manchester United in the league this weekend, but he wants his players’ minds firmly focused on the visit of the League One side.
“We’ve got a game on Tuesday night so there’s no thoughts towards Manchester United yet,” the Northern Irishman said.
“We’ve got a game in the cup that we want to progress through. There’s no doubt winning games breeds confidence — the players are only getting the rewards for how hard they have been working.
“We had a really good pre-season, the focus in the team is very good and we were determined to make a good start. It’s only two games, it’s very early yet, but it’s better to win them than draw or lose.”
There are 17 other matches in the competition on Tuesday night.
Hull travel to in-form League One leaders Leyton Orient and Tigers manager Steve Bruce is expected to ring the changes.
Bruce is without Yannick Sagbo who is suspended after being sent off in Saturday’s win over Norwich, while he could take the opportunity to rest new signings Tom Huddlestone and Jake Livermore.
Steve Harper is set to make his Tigers debut in goal and there could also be starts for the likes of Danny Graham and Liam Rosenior as Bruce keeps one eye on Saturday’s trip to Manchester City.
Record signing Dani Osvaldo could make his first Southampton start in their tie at Barnsley.
The Italy international striker was a substitute in the weekend draw with Sunderland but could be given the nod from the off at Oakwell.
Crystal Palace boss Ian Holloway has made it clear he intends to shuffle his pack for his side’s trip to Bristol City.
Several summer signings are among the players who could come into the team to face the League One outfit, such as goalkeeper Neil Alexander, defender Florian Marange and midfielder Elliot Grandin.
West Brom goalkeeper Ben Foster will miss his side’s clash against Newport after suffering an ankle injury in Saturday’s Premier League draw at Everton.
Third-choice keeper Luke Daniels, who replaced Foster at Goodison Park, is ready to step in but regular back-up Boaz Myhill is hopeful of overcoming a wrist injury.
Fulham forward Hugo Rodallega is set to make his first appearance of the season at Burton.
Cottagers boss Martin Jol has said he will make “a few changes” for the clash with the League Two side and mentioned Rodallega and midfielder Ashkan Dejagah, another player who has not had any Premier League game time so far this term, specifically.
Goalkeeper Maarten Stekelenburg (shoulder) and defender Kieran Richardson (hamstring) remain on Fulham’s casualty list.