Gerrard was in inspired form as he scored twice from the penalty spot to lead Brendan Rodgers' side to an impressive 3-0 win at Old Trafford, with the England skipper even able to miss with a third spot-kick as he smashed the ball against the post in the second half.
He told Sky Sports: "We came here to win the game, it's difficult and we need to take each game as it comes. We'll enjoy tonight but we have to move on quickly. We have shown today we are genuine contenders and we'll fight for this.
"We believe it [that Liverpool can win the title]. But I've said it many times - in football the easiest thing is to talk the talk. We've got to go and treat Cardiff like Manchester United now.
"And then we've got to treat Sunderland like Manchester United and if we do, we'll win a lot of games from now to the end of the season. So the rest of the people that are fighting for it, with us, have got to believe we're going for it."
Gerrard also hailed the performances of Daniel Sturridge and Luis Suarez, who scored his side's third goal at Old Trafford, adding:
"I've come here many times and been played off the park, they're a fantastic team. To come here and dominate from start to finish. We go away slightly disappointed we didn't get more goals.
"You have to credit the manager, we played a diamond today and totally bossed the middle of the park and when we do thatm we have two of the best strikers in the world to do the damage.
"If you ask the United defenders, I'll bet they'll say they haven't had a harder 90 minutes than today."