The Reds recorded their first victory at Old Trafford since 2009 - and only their 16th league win on the ground in 118 years - with a comfortable 3-0 triumph over Manchester United.
Gerrard scored two penalties and hit the post from a third before Luis Suarez completed the scoring.
"We showed today that we are genuine contenders and we are going to fight to the end for this," Gerrard 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 (their next match) 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."
Rodgers will not publicly declare his side can win the title but he is happy for others to say so on his behalf.
The trip to Old Trafford was seen as a defining moment for their hopes of a first title since 1990 with Chelsea losing at Aston Villa on Saturday.
They did not disappoint as United were swept aside with consummate ease but the Reds boss still will not get excited about the title.
"I've not banned it (talk of the title). We have better things to talk about," he said.
"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 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."
Rodgers was delighted with the way his side took the game to United and never relented and while they may have been fortunate to be awarded a third penalty he did not think they were lucky to be 3-0 winners.
"I thought we were outstanding; from the first whistle our intent was to attack and press and to work. Clearly I am very happy," he added.
"I thought we could've had more goals. We were really aggressive in our game going forward and had it not been for that final pass and touch we might have got in better and finished them off even more so."
Sturridge fortuitously won one penalty, which resulted in Nemanja Vidic being sent off, but should have had another one after that.
"I thought that was probably the clearest one," said Rodgers.
"Daniel got tripped clearly and it should have been a penalty.
"It (Vidic's sending-off) was harsh. From both perspectives Vidic isn't going to get back and Daniel has a choice he either stamps on him or tries to hurdle him.
"We are a team who gets penalties because of our aggression in our attack."
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