The 23-year-old moved to the Reds from La Liga champions Real Madrid on a season-long loan deal, opting to join the Merseyside outfit despite interest from Arsenal.
The Turkey international completed 93 per cent of his passes in a promising display, and Rodgers is confident Sahin will improve as he reaches full fitness.
“He hasn’t played a lot, Nuri, so to get 65 minutes was good for him. He showed he is an accomplished footballer and that he’ll be able to fit in really well into our style,” Rodgers told Liverpool’s website.
“He’s a good guy and as he gets fitter and stronger he’ll become better.”
Rodgers also admitted his side looked tired after playing their third game of the week as goals from Lukas Podolski and Santi Cazorla secured victory for Arsenal.
The former Swansea City manager was pleased by his players’ commitment, but Rodgers wants Liverpool to improve their ball retention after sloppy passes led to both of the Gunners’ goals.
“For a lot of them, that was their third game [in a week] – three tough games in Manchester City last week, Hearts and then this game,” he added.
“They’d put everything into it and I can’t ask any more from them.
“In spells of the game, we played ever so well, maybe never took our chances when we had the opportunities and obviously we then suffered by conceding two disappointing goals from our point.”
Rodgers added: “We need to keep the ball better. For me, it’s a crime when you keep losing the ball and that was unfortunately something we did, particularly in the second half.
“We always have to improve and it’s going to be important technically that we keep the ball because if you don’t then it can cause you a problem.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news