The Uruguay international, who has faced a number of disciplinary issues since moving to Anfield in 2011, has scored three goals since returning from a 10-match ban a fortnight ago.
"That attitude from Luis to demand the best is exactly what we want," the Liverpool Daily Post quotes Rodgers as saying. "We can't accept just winning and say it's all right.
"I think it's much easier to keep on performing well and, if you do lose, then you can still go into the next game with confidence, but if your standards slip and you start losing one or two games, it's a lot harder to get back up to the level again.
"With the likes of Luis, that demand is what we want – the demand that we maintain our standards at all times. It is an important part of what we are trying to do."
The 26-year-old expressed his desire to leave Merseyside during the summer, but Liverpool blocked the striker's exit.