In the story "The Fall of the House of Usher," Poe employs the supernatural as a figment of Roderick's imagination to show his crumbling sanity. The main character's behavior is increasingly neurotic and erratic, and as he starts to succumb to his perception of supernatural events, he begins to act worse and worse.
As he is reading a story in his house at one point, ominous and mysterious sounds begin to present themselves to his ears. This is all a figment of his mind, but he believes the supernatural cacophony is occurring in reality around him. Eventually, he comes to believe that his sister has been buried alive, and when it is revealed that he is correct, through some mysterious happenstance, she attacks him and they fall down dead. The narrator at this point flees the scene, which collapses behind him. The supernatural elements create a state of mysticism and confusion that drive Roderick mad.
The two distinctly supernatural elements in this short story are Madeline's bloody emergence from the crypt and the collapse of the physical house of Usher into the tarn on the death of Roderick and Madeline.
I would turn the question around to say that the neurosis narration that precedes these two dramatic ending events is what makes them seem plausible to us. There is a dramatic buildup that emerges from Roderick's neurosis or deeply nervous and acutely sensitive personality that prepares us for what is to come.
Roderick's nervousness when the narrator first arrives seems disproportionate to any reality. His sister is dying, but beyond that, there seems to be no reason for him to be as highly strung as he is. He is acutely sensitive to light, acutely sensitive to sound, can bear only certain kinds of art, and seems intensely on edge. This primes the reader to wonder what he knows or intuits of a supernatural quality that we don't. By the time we do encounter the supernatural, Roderick's neuroses have strongly foreshadowed the denouement: his neurotic premonitions and forebodings seem now to have been justified. The narrator seems to believe this as he flees the house: he is not going to wait around and see if things will normalize. Like him, we know they will not.
The narrator in Edgar Allan Poe's "The Fall of the House of Usher" is presented initially to the reader as a very rational man. As with most of Poe's narrators, he speaks with an elevated diction in order to gain the trust of the reader, coming across as someone who is mentally stable and capable of reason. When he first comes to the house, he notices many of its oddities from the outside, as well as the distressing impact they have on his demeanor; however, he seeks to explain this effect through logical means, considering how "there are combinations of very simple natural objects" that have such perplexing effects on people.
In order to create a truly neurotic narrator, however, Poe continues to elaborate on the oddities of the house, imbuing it with seemingly supernatural qualities and even powers that continue to grate on the narrator's mind. The most prominent example occurs after his head has been filled with all of Roderick's suspicions about the house being alive. He begins to read Roderick a story in order to calm his nerves. As he reads the story, he notices strange noises that correspond to the descriptions in the story he is reading. He ignores them at first, but eventually they become so prominent that he accepts them as inexplicably real sensations. The more he reads, the more neurotic he becomes as he must forsake his rational and scientific mindset in order to come to grips with the reality he is experiencing.
Eventually this reaches fever pitch when Roderick admits that he believes they have mistakenly buried his sister alive. When his sister is revealed to still be alive, and she attacks Roderick, the narrator can no longer reckon with the events he is witnessing. He runs out of the house as it, along with his own mental stability, crumbles in his wake.