Sterling, who is just 17, opened the scoring for the Reds at Anfield before strikes from Lucas Leiva and Carroll secured their win over the German side.
And, despite Carroll being linked with a move away from the club this summer, Rodgers had kind words for the attacking duo in his post-match press conference.
“I was pleased with (Sterling’s) goal as a whole,” he told reporters. “We had pressure on one side of the field when we won the ball and we took the ball out of the pressure zone and changed the game.
“I like the wingers to play with width and by the time it got to Enrique he was in a great position but his movement off the ball was very impressive.
“(He showed) the imagination and creativity that I love – the cut inside and a wonderful finish. The boy’s a talent with still a lot to do and a lot to learn but he’s certainly shown over this pre-season he now worries about the team and the responsibility.
“Big Andy showed his skill and ability. He probably gets a bit of stick that he can’t play this way but it was a wonderful piece of skill to let it go through his legs and get the shot on target and he tucked it away very well.”