What is the supernatural element of Tell-Tale Heart?

Until we analyze what the narrator is experiencing, it does seem as though there is a supernatural element to the story; however, what at first appears to be supernatural can actually be explained naturally. After the narrator has murdered the old man, dismembered him, and buried him beneath the floorboards, the police arrive to investigate the old man's cry, which a neighbor heard in the night. While the officers are there, the narrator believes that he can hear the old man's heartbeat from underneath the floor. However, we know that this is not possible because, for one reason, the old man is certainly very dead. The narrator's description of the sound helps us to identify its natural cause. He says,

It was a low, dull, quick sound –– much such a sound as a watch makes when enveloped in cotton.

We know that the narrator's adrenaline is racing because he fears discovery. Earlier in the story, when the narrator was about to murder the old man, he believed that he hears the man's heartbeat. He said,

[...] there came to my ears a low, dull, quick sound, such as a watch makes when enveloped in cotton.

His adrenaline was racing then, too. As his fury grew, he said, the sound "grew louder, [...] louder every moment." Thus, we can interpret this sound as the narrator's own heart beating. It is not possible to hear another person's heart beat from across the room with one's naked ears, and it is not possible for a person's heart beat to continue after they've died. Therefore, there is no supernatural origin of the heartbeat, just a misguided and mentally ill narrator who misinterprets his own heartbeat.