Sea anemones are members of the phylum of Cnidaria. Distinguishing features of this phylum are radial symmetry and the presence of cnidocytes, or stinging cells (like the ones found in jelly fish). These cells have a mechanical trigger and if activated a subcellular harpoon is fired and paralyzing and painful toxin is injected. A cnidocyte diagram is shown below (from Wikipedia):
The Cnidarian nervous system is relatively simple indeed. The Cnidarian nervous system is decentralized and diffuse, and it basically consists of reflex arches. It is referred to as a "nerve net" as shown in the following schematic of a sea-anemone's nervous system (picture from Florida Int. University):
The presence of cnidocytes and a mesh nervous system basically answer your question:
1) Feeding: Whenever a prey touches the sting cells, it gets harpooned and paralyzed. The mechano-sensory cells sense touch, and drive nervous cells in the mesh. The nervous cells activate contractile epithelial cells in the arms of the anemone that push the prey inside the mouth. Then digestion takes place and the mouth serves as anus once digestion is complete.
2) Defense: the cnidocytes operate by mechanical triggering and no nerve cells are necessary.