Sturridge has scored seven goals in eight games for the Reds so far this season, helping re-establish Liverpool as a contender at the top of the Premier League following a January switch from Chelsea.
Rodgers told The Guardian: "I think any player wants to feel he belongs. You can't do it on your own in this game anyway. Daniel feels very much a part of a team now. You only need to see how hard he is working and how committed he is.
"Tactically he has been very good in the games. What we are asking him to do without the ball. He feels very much a part of the side and around the place he looks very happy to be here.
"He is proud and knows the size of the institution that he is playing for. He's a top player. He's 24 now and he is only just getting the chance to show consistently that he can play with the best."