The Uruguayan striker has scored three goals in three outings since making his first start in the Capital One Cup loss to Manchester United on September 25 and Rodgers is happy with how he has gone about business despite missing the first part of the season.
"With Luis, he demands the best from himself and his teammates at all times and we saw that against Crystal Palace, even right at the end, when the game was won," Rodgers told the club's official website.
"You see his work-rate and his demand for a better ball into the box - and that's what we want.
"There was a moment in the first half where he chased back on the left and won the ball, too. There is no doubting his commitment and there is no doubting he will always have that desire at all times."
He added: "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."
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