Brendan Rodgers' side moved five points clear of Chelsea, who they host next weekend, with a hard-earned 3-2 victory at relegation-battlers Norwich on Easter Sunday.
It was an 11th straight league win for the Reds, and one which took the Merseyside club another step towards lifting the top-flight trophy for the first time since 1990.
While the fans might be draping banners over the walls at the club's training complex and whipping up the atmosphere when the team coach rolls into Anfield, Sterling insists the players must all just focus on the job in hand and not on the ultimate prize which is now so tantalisingly close.
"We come in every day at Melwood and see each other, everyone knows what the dream is at the end of it, so everyone is just keeping each other modest and we know that if we keep working hard there is this real goal at the end of it now," he said.
"I just think the important thing is for us to keep our heads down, keep working again this week, then go again this weekend."
Sterling helped lead the Liverpool attack, which was without injured forward Daniel Sturridge, in impressive fashion as he cut inside from the left to fire a 25-yard drive past John Ruddy which put the visitors ahead after only four minutes.
The England World Cup hopeful then set up Luis Suarez on 10 minutes as the Uruguay hitman swept home the 30th goal of his superb season.
Liverpool manager Rodgers hailed 19-year-old Sterling as "arguably the best young player in European football at the moment", with the forward last week shortlisted for the upcoming PFA awards.
Midfielder Lucas is in no doubt Sterling can continue his progress.
"He is showing he is developing and improving all the time," the Brazil midfielder said.
"Raheem is playing with no fear, players normally have ups and downs, but he is really consistent and has probably been our best player over the past few months."
While the Reds close in on a jubilant end to the campaign, Norwich are left staring at the abyss following a third successive defeat.
The Canaries are in 17th, and have to hope all the sides below them fail to close the three-point deficit or they can somehow pick up something from a daunting run-in away to first Manchester United and then Chelsea before Arsenal head to Carrow Road on May 11.
Norwich sacked manager Chris Hughton in the aftermath of the home defeat to West Brom, and at least Neil Adams - promoted from the academy set-up - was able to get his team to show some fight in the second half against Liverpool.
Gary Hooper's first goal since Boxing Day reduced the deficit and, after Sterling had put Liverpool 3-1 ahead, Robert Snodgrass made sure of a tense finale with a looping header.
Scotland winger Snodgrass believes if Norwich can sustain that level over 90 minutes then they can take something out of the final three fixtures.
"If we did not realise before, well we are bang in it now, there are three teams who can catch us," he said.
"It is now who wants it the most, who wants to keep the club in the Premier League.
"We need to look at ourselves and focus on ourselves because other results are not going to get us out of the trouble we are in.
"We will need to give the performance as we did in that second half against Liverpool, nothing less, and hopefully we can stay in the Premier League.
"We have to maximise everything we have in the tank - heart, desire and endeavour all needs to be there, if we have got that, then the chances will come and hopefully we can take them."