City came from one goal down to record a 2-1 victory over the Blues at the Etihad Stadium to set a new Premier League record for consecutive home wins.
That result moved them back to within one point of Manchester United at the top of the table with nine games remaining, but Richards is keen to ensure they keep pace with their rivals when they head to the Britannia Stadium.
“Three points against Chelsea will not mean a lot if we don’t back it up with a win at Stoke,” he told Manchester City’s official website.
“Stoke is one of the most intimidating and loudest grounds we visit in this country and it is never an easy place to go and win. We have to be at our absolute best."
Richards has been forced to fill in at the heart of City’s defence in recent weeks due to the absence of usual centre-back pairing Joleon Lescott and Vincent Kompany.
While Kompany looks likely to be fit for Saturday’s encounter against Stoke, Richards says he is willing to carry on playing out of position if called upon to do so by manager Roberto Mancini.
“The manager will decide when and where I play and I will get on with it,” he commented.
“We have a great squad of players here and we will all play our part between now and the end of the season, I am sure of that.
“It was really good that Carlos Tevez came back and that most people got right behind him. He can be inspirational and I am sure that like all the players he will have his say between now and the end of the season.
“We felt we showed great tenacity against Chelsea, we showed everyone what fight and belief there is in this team; now we have to show that nine more times.”