The England international was instrumental in the Merseyside club's push for the Premier League title last season, but has scored only three goals in the current campaign.
Sterling turns 20 on Monday and Rodgers believes he has made great strides despite Liverpool's disappointing season so far.
He said: "He has taken on extra responsibility, absolutely, and kicked on. I have reiterated to him his qualities and strengths, his pace, skill, his directness – that's his game,
"I think you have seen him develop into a very good young footballer. He's not just someone who can run direct with the ball, he can play one-touch, he can play two-touch. He's such a threat.
"You looked at him the other night [against Leicester] against the boy [Ritchie} De Laet, who is a super-quick player. Raheem's pace was frightening.
"His runs were very good and at 19, nearly 20, I think he's shown he has gone to an extra level."
Much was made of Sterling declaring that he was tired before England's Euro 2016 qualifier in Slovenia in October, which led to him being left on the bench by Roy Hodgson.
And Rodgers has stressed the importance of ensuring his prodigy does not play too many games at such a young age.
When asked if Sterling will need a rest from time to time, Rodgers said: "There will be a period where we will do that - it was always in the plan.
"Of course there is the short term, but you have got to think in the longer term. He's a kid coming off the back end of a long season where he played a lot of games, and then go on travelling to a World Cup.
"He's a young player coming back. I think a lot of the players that were away and coming back, it takes a bit of time to get going again."
