The Uruguayan forward scored his first-ever hat-trick at Anfield as the Reds tore the Baggies apart to stay within two points of Premier League leaders Arsenal.
"It was a difficult summer for him but it was for everyone and we managed as a club and he has managed himself well and he has come out the other side performing as he always done," PA Sport quotes Rodgers as saying.
"I knew once I had got the commitment from him in the summer he has been great. He is a tireless worker and I knew if he stayed it was going to be the case of working in training as he's always done.
"It was his first hat-trick here at Anfield, I think you have seen his commitment to the team and what we are trying to do. It was a wonderful performance. Magic."
The 26-year-old has now scored six league goals this season.