This is actually an interesting question, because the narrator of the poem--who we are used to being the good guy--is also the man who commits murder. He would like us to think that he is the good guy--a blameless, completely sane person who did only what anyone else would have done in his situation. He would have us believe that he is the brave protagonist, and the old man with the evil eye is the antagonist; after all, that eye certainly did antagonize him. Looked at in that way, the narrator is the protagonist and the old man (or his eye, even) is the antagonist.
The protagonist to a story usually is the character around whom the action is centered; in this case, that is the murderous narrator. However, usually the audience is supposed to be able to relate to the protagonist, and traditionally, he is thought of as a hero. I don't relate to a clearly insane murderer, nor do I think he is a hero, so that is where this question becomes tricky--yes, the narrator is the protagonist, but we certainly don't like him or relate to him. I also don't think that the old man (or his eye) were classic antagonist; he isn't actively contending against the narrator. He isn't going out of his way to create conflict and chaos in the narrator's life--he simply exists. So the old man is not your classic antagonist either.
This poem definitely tests the boundaries of our definitions of protagonist and antagonist; that's just one more reason it is so interesting. I hope that those thoughts helped; good luck!