The England international scored his second Premier League goal, with Luis Suarez adding two more, as Sunderland were dispatched 3-0 at Anfield.
Sterling, who has featured in 20 of the side's 21 top-flight matches, turned 18 less than a month ago and soon after signed a lucrative five-year contract.
Yet less than 18 months ago he was playing in Liverpool's youth teams.
"I try not to take in what people are saying and just listen to the manager and the people who have influenced me to play football," said the teenager.
"Hopefully I can just do well and not let it take up too much of my head, just play my normal game and goals and assists will come.
"I don't really listen to anyone apart from people at the football club.
"It is a big step for any 17-18-year-old to come and play in the Premier League with players like Steven Gerrard and the expectation is going to be high week in, week out.
"But as a young player you just have to keep playing."
While Sterling showed composure beyond his years in front of goal the two players who ran the show against the Black Cats were Suarez and Gerrard.
The latter was given far too much time and space by the visitors to be able to work the ball around at his leisure and his 60-yard pass for Suarez's second was trademark Gerrard.
"They are the players who make the difference - but they need the other players around them," said Rodgers.
"The captain, over the four games he has played over this period, has been absolutely phenomenal.
"You won't see a better pass than that this season, it was phenomenal and an incredible performance by him.
"His performance level has been fantastic and he has really taken to the ideas and is learning a new way of playing and you see him flourishing."
Inconsistency has dogged Liverpool throughout the season as they have not been able to put together a run of games to get them close enough to be considered genuine top-four contenders.
However, Wednesday night's win moved them up to eighth, seven points behind fourth-placed Chelsea, and the arrival of £12million striker Daniel Sturridge from Stamford Bridge gives the manager hope for the second half of the season.
"Nine points out of 12, over a real busy period, we'd have probably taken that," said the Reds boss.
"And it's six goals, two clean sheets and two outstanding performances since the Stoke defeat (on Boxing Day).
"You have to give massive credit to the players because the effort, as well as the quality, they put into the game was phenomenal.
"Our superiority in our game was very good and I am very pleased.
"I believe second half of the season we can up the tempo and kick on.
"It is about consistency and hopefully we can find that over the coming months and years."
On Sturridge Rodgers added: "He has come in to be competitive.
"He will come in and learn from everyone. He will not learn only about football, he will learn about being a top human being.
"His hunger is the biggest thing for me - it's the biggest we have at this club.
"And if you are away from home and you haven't got that control or domination of the ball he is brilliant on the counter-attack."
With Joe Cole West Ham-bound Rodgers does not have much else lined up just yet in terms of new arrivals.
"There is nothing in the pipeline, it was never going to be a busy month," he said.
"We are not just going to spend needlessly. The young players have gained great experience but we need to improve the depth.
"The idea is to retain our consistency and we have done that last night by getting a great start to 2013."
Sunderland manager Martin O'Neill blamed fatigue for his team's defeat, the second in succession after losing to Tottenham.
"Being unable to shuffle our pack a great deal the fourth game really caught up with us," he said.
"We are going to have a look (in the window). I think we would need some reinforcements.
"With Wes Brown and Lee Cattermole injured we don't have much more choices than what we had.
"John O'Shea has a hamstring injury and although it is improving I can't give you a definite time on that but he won't be fit for Saturday."
On the outgoings O'Neill added: "Hull City have made an offer for David Meyler, which is one we have considered and might even accept and there is not much more I can tell you on anything else."