Playing on the left, Sterling chose his moment to wander into a central position ready to latch onto a Luis Suarez throughball.
He then kept his composure to slot past goalkeeper Alex McCarthy.
Afterwards Rodgers told liverpoolfc.com: "It's a part of the game we've been working on. The players on the outside, the No.7 and No.11, we're trying to get them in the positions so they can make those runs.
"He's got good pace, Raheem, so once he's on the inside he can break the line of the back four.
"We've been doing a lot of work on that on the training field but all the credit goes to him because he's got to identify the moment to go in.
"It was a wonderful finish because he was going away from the goal, and he's got a quick defender tracking him.
"He's a terrific talent and he's got a good head on young shoulders."