Rodgers replaced the beloved Kenny Dalglish in the Reds hot seat this summer but has failed to win any of his opening three Premier League games.
His lack of activity in the transfer market has also worried the Anfield faithful, with long-term target Clint Dempsey joining Tottenham Hotspur on deadline day, 24 hours after striker Andy Carroll left on loan to West Ham United.
However, Rodgers is not downbeat about his side's performances thus far and has pleaded with the Liverpool support to give the new regime time.
"The message is to keep the faith," he told Liverpool's official 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.
"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."