Rodgers said the 26-year-old's intention to change had not reduced his desire on the pitch, highlighted by his hat-trick in the win at Wigan last weekend.
"There is no correlation. He has a will to win," he said.
"There are cultural differences to where he has worked and played before and you can see he has clearly adapted to that.
"He was struggling a bit with an injury last weekend, believe it or not, and nine out of 10 players wouldn't have played but his threshold for pain is so high.
"He wanted to play and to have someone like that in your team gives you great hope and gives great inspiration to other players because he really wants to win for Liverpool."