The Merseyside outfit are preparing to face Bolton Wanderers in a FA Cup fourth-round replay at Reebok Stadium on Wednesday - a week on from their painful 2-1 aggregate loss to Chelsea in the League Cup semi-finals.
Liverpool's hopes of making the final were dashed in the fourth minute of extra-time, Branislav Ivanovic's thumping header proving the difference at Stamford Bridge.
That late defeat represents Liverpool's only loss in 12 matches in all competitions and Rodgers is backing his players to make a charge towards the FA Cup decider.
"Obviously after that game [against Chelsea], there's a feeling that maybe it would disrupt or provoke a negative reaction to our season," Rodgers told reporters.
"But if anything, it's only promoted the development and the momentum that we have. Of course we wanted to get through to the final. But the performance level over the two games and leading into those games has given us great encouragement that our best football is yet to come."
Rodgers, who oversaw Liverpool's goalless draw at home to Bolton on January 24, added: "There are still good teams in it [the FA Cup]. As I said, it only counts if we get through ourselves.
"So for us it's looking at the Bolton game and it being a tough game but for sure you get through each game and it optimises your chances of getting through to the final.
"We're in two competitions now [the FA Cup and the UEFA Europa League]. Two cup competitions and we want to go as far as we possibly can in them.
"That will be reflective in our teams and in our drive and desire to get through in the competition."
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