The Northern Irishman hailed the attacking duo after their strikes in Sunday's friendly victory and expressed his delight at linking up with midfielder Joe Allen again
17-year-old Sterling opened the scoring for the Reds at Anfield, before strikes from Lucas Leiva and Carroll added a deserved gloss to the scoreline.
And, despite his No.9 being strongly 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 [with the goal]. 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."
The Northern Irishman also praised the Reds' latest acquisition, Wales international Joe Allen, whose £15 million move from Swansea was confirmed on Friday but did not feature at Anfield.
"Joe will fit into the group very well," he added. "I like technically gifted players and he's exceptionally technically gifted.
"I also like good people and he's a very humble young guy who knows he's 22 years of age and has an awful lot to learn but he will be with us every single day in the journey to make this club better."
The 39-year-old went on to hail his side's performance against the Bundesliga outfit, who are managed by Reds legend Sami Hyypia.
"I thought the players were excellent today, especially on the back of a game on Thursday night," he added.
"I'm very pleased, I see the idea of the team improving each time we play and in a very short period of time the players are taking on board that tactical concept of controlling and dominating the game.
"Last time Bayer Leverkusen were out they won 7-1 against [Eintracht] Frankfurt so for us to play with that control and domination against a very, very good side was excellent.
"So we arrive into next week with a clean bill of health, everyone's training and they're really embracing the work, it’s great to see."
After laughing off rumours of a Manchester City bid for Daniel Agger, the former Swansea boss also insisted that he still faces a battle to win over the club's fans ahead of their Premier League season beginning against West Brom next week.
"I do feel at home but I will never be complacent," he continued. "I have got so much to prove here; I've come in and I'm sure that the majority of supporters aren't sure about me.
"I've got to fight for my life here to prove that I'm good enough to be here but I certainly feel comfortable in relation to my position and my work on the field.
"My promise was to fight for the club every single day so we're in a good moment, a good position and it's been a terrific pre-season.
"We've already started our competitive games in the Europa League and we now arrive into the Premier League next week and real strong mindset and hopefully that will continue."