"The Raven" by Edgar Allan Poe is a poem in which the narrator, a student, sits alone mourning the death of his beloved Lenore. Because we do not have a full story with multiple characters, but only a dialogue between the narrator and the bird, there is really no sense of a traditional conflict between a protagonist and antagonist, unless one wants to consider the raven itself as an antagonist.
While it is true that the student is somewhat frustrated by the bird's one word vocabulary of "nevermore," the relationship between the raven and the student is really not one of true conflict but rather the student projecting his own despair onto the bird. The other struggle in which the student engages is with his own despair at the death of Lenore, but the actual event of her death occurs before the start of the poem.
"The Raven" is a poem rather than a story, and, according to Poe's own "Philosophy of Composition," intended to illustrate a moment of intense of emotion rather than an extended narrative, and thus really has no need of a narrative conflict.