Reds captain Steven Gerrard, who scored two penalties and hit the post with a third, believes Sunday's 3-0 win at Manchester United means Liverpool are genuine contenders along with Chelsea, Arsenal and Manchester City.
Rodgers has long played down the likelihood of his side winning a first league championship since 1990 and does not intend to start promoting their chances now, although he is happy for his players to use it for inspiration.
"I've not banned it (talk of the title). We have better things to talk about," he said after Liverpool moved back into second place, four points behind Chelsea with a match in hand.
"It is about improving and getting better. I don't lose sleep over it.
"We are up there on merit so of course we have an opportunity.
"I didn't say [we have] no chance. If you think we have a chance then write it.
"I try to not expect so much and let the players do the talking. We try to remain dignified in our work and our players are doing all the talking.
"We will focus on the next game against Cardiff. I think other teams will drop points - we may well drop points, we may not - but I can only look at our next game and I've done that since I walked through the door and I'm not going to change."
Liverpool recorded their first victory at Old Trafford since 2009 and only their 16th league win on the ground in 118 years thanks to Gerrard's penalty brace and a late third from Luis Suarez.
And a fired-up Gerrard was certainly more bullish than his manager when asked what the final nine matches of the season may hold in store.
"We've showed that we are genuine contenders and we are going to fight to the end for this," he told Sky Sports 1.
"We believe it but I've said many times that in football the easiest thing to do is talk the talk.
"We've got to go and treat Cardiff like Manchester United and we've got to treat Sunderland like Manchester United.
"If we do we will win a lot of games until the end of the season. The rest of the teams around us have to believe we're going for it."