The 39-year-old’s side slumped to a 2-0 defeat by Arsenal at Anfield on Sunday, with the Reds yet to claim three points following a 3-0 defeat at the Hawthorns and a 2-2 draw with Manchester City.
Rodgers, who replaced Kenny Dalglish in May, admitted his players were tired after a demanding week but has promised his side will improve.
“The message is to keep the faith,” Rodgers told Liverpool’s website.
“West Brom, the first half was very good; we showed in the Manchester City game that we could be competitive; and then against Arsenal we weren’t quite at our best. There are a number of reasons for that, a lot of players were playing their third game in a week and you could see that played a part.
“It’s still very, very early on. We hope as time goes on we progress and can improve.”
Rodgers also moved to alleviate concerns about Liverpool’s goal scoring problems after the Reds failed to bring in a striker to complement Fabio Borini and Luis Suárez on deadline day.
“It’s something you continually work on all the time,” he added.
“We’re still getting the balance in a couple of areas of our game. We build the game very well through the thirds, but it’s about making sure that when we arrive in the final third, if we can’t find the moment to score straight away, we maybe have to have that wee bit more patience.
“That has a knock-on effect to the team. When you are that little bit more patient at the top end of the field, everyone else behind that then can get into position.
“We’ve created enough chances to score goals in the games. That’s been pleasing.
“It’s finding that football intelligence at the top end.”
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