The new Anfield boss on Sunday oversaw a 3-1 victory against Bayer Leverkusen on Merseyside as the Premier League club concluded their pre-season with a win.
Teenager Raheem Sterling opened the scoring in style before Lucas Leiva took another step on his return from injury with a goal and substitute Carroll then added a third.
England international Carroll is not thought to figure in Rodgers’ plans and the £35million striker is a target of West Ham United, while a return to Newcastle United is also possible.
“We arrive into next week with a clean bill of health, everyone is training, and they are really embracing the work and it’s great to see”
But Rodgers thinks the tall and powerful 23-year-old, who has been accused of only being able to play in a direct system, showed good skill when turning and firing a comparatively straightforward shot which was fumbled by Leverkusen goalkeeper Bernd Leno.
Rodgers said of Carroll on Liverpool’s official website: “It was a terrific goal from him. It was a nice, clever piece of play by Charlie Adam as the ball came into him and he flicked it around the corner.
“Maybe eight or nine times out of 10 he would have expected that (the ball) back, but big Andy showed his skill and ability as well.
“He’s got stick that he can’t play this way, but it was a wonderful piece of skill letting the ball go through his legs, getting the shot on target and tucking the ball away very well. It was very pleasing all round.
“The players had a wonderful idea of the game tactically and I am seeing an improvement every single day in terms of our passing game.”
Rodgers’ £15million signing, Joe Allen, was in the stands at Anfield to watch the win over Leverkusen having followed his manager to Liverpool from Swansea after a transfer was confirmed on Friday.
And Rodgers, who had already signed another former Swansea player in Fabio Borini, remains determined for the Wales international to not be the final new face at Anfield before the end of August.
He said: “Joe will fit into the group very well. I like technically gifted players, and he is exceptionally technically gifted.
“But I also like good people and he is a very humble young guy. He knows he is 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.
“He is a very talented boy and he comes into an excellent group. Hopefully we can add one or two more before the end of the window.”
Full of praise
Rodgers was also full of praise for Brazilian midfielder Lucas, who was ruled out from last November after suffering a serious knee ligament injury.
He joked: “He has been brilliant. He is a terrific guy and he is prolific from seven yards with no goalkeeper!
“You have seen the growth of him as a player and a person, and the journey he’s been on at this club is incredible. He still feels he has a lot to offer. How I work in liking to play this high, intense pressing and passing game brings on his fitness.
“I think if you look at him now, he is in a real good moment. Hopefully he can stay fit and strong and keep pushing on for us.”