The Uruguayan has scored 20 times this season but Liverpool are still seven points adrift of fourth place.
"Luis had a terrific season last season and he had an opportunity to leave, and probably would have had an excuse with a new manager coming in, but he didn't. He committed to the club," Rodgers said.
"He sees the vision going forward, and he believes in that. He knows it won't happen overnight. He has had a brilliant season with 20 goals until now, and hopefully there are many more to come."