The Merseyside outfit have made their worst start to a season in 101 years, with the new manager still yet to clinch a Premier League victory at Anfield in four attempts.
However, Cole believes the club have all the tools to once again challenge at the right end of the table and insists Liverpool just need time to settle after a tumultuous summer.
“I’ve seen the team developing and I’ve seen a lot of improvement, but revolutions don’t happen in days and weeks,” he told the Liverpool Echo.
“The fans here are great and they understand what’s happening. They are very educated - they know what we’re trying to do and how we’re trying to build the play and implement a style.
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“They know it’s just a case of being patient. The performances have been good and we deserved the three points against Stoke.”
Rodgers moved to Anfield after an impressive debut season in the Premier League with Swansea City in which he guided the Welsh club to an 11th-place finish using a regimented passing style often compared to that of the so-called ‘tiki-taka’ made famous by the current Barcelona side.
And Cole has backed Rodgers to successfully implement that tactical style and bring success to Anfield.
He continued: “We just have to concentrate on trying to implement that style.
“We have to keep doing what we’re doing and keep working hard - and these things take time. The performances have been good considering everything has changed here.
“The lads are responding well to what we’ve been asked to do. Of course we need to start winning more games but I can see only positive things.”