They last won 1-0 against promoted side Bournemouth on Aug. 17 and are 13th in the table with eight points from six league games.
Liverpool drew with Bordeaux in Thursday's Europa League match and were held 1-1 at Anfield on Sunday by a promoted Norwich City.
The Merseyside club have scored only four times this season, the second lowest in the league, and their slump in form has coincided with the loss of captain Jordan Henderson, who faces up to two months on the sidelines after breaking a bone in his foot during a training session.
Rodgers was confident that the team would soon return to winnings ways.
"Hard work pays and it's just going to be a matter of time until they can get the results to be rewarded by that. I think (confidence) will grow with results," the 42-year-old told the club's website (www.liverpoolfc.com).
"We just have to build that confidence through our training, through the games, and it's just step-by-step, getting to the next game and hopefully a good performance and keep getting results.
"It's certainly something that we're embracing and the players, I'm sure, if they continue to work as they have been on a daily basis, they'll get their rewards," the former Swansea City manager added.
Liverpool, who face Carlisle in the League Cup on Thursday, will be eyeing three points when they host 17th placed Aston Villa two days later.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
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