No, you don't need to feed corals, they should be alright with the right lighting and water conditions. You can cause more problems over feeding your tank of you feed to much. Don't get confused though, this is not a coral. An anemone is an invertebrate. He just looks like he is upside down, did he fall off the glass? If that's the case then pop him back the right way up on a rock. They like a lot of light and a lot of flow. You didn't say what kind of lights you have?