The 20-year-old scored a second-half winner during a hard-fought victory for the Anfield side, taking his chance clinically as opposed to his profligate performance at Manchester United two weeks ago.
And Rodgers believes the Liverpool forward's improvement in front of goal shows how well he is adapting to playing up front.
"It shows what a great learner he is," the Liverpool boss said of Sterling. "He is in a position now where he's going to receive a lot of opportunities in that type of situation, because of his pace - which will take him away from anyone.
"He's going to get those central runs, running onto the ball. Because he's playing in that position, he's gone away with the coaches and worked on that type of finish, both left side and right side.
"He showed great composure and he showed great ability to learn, to beat the 'keeper and finish it really well. His development and ability to want to be better has got us the three points."