While some Poe stories have a kind of fun and playful feel to them in spite of their themes of death, murder, and betrayal, "Tell-Tale" makes us want to cry, run screaming from our chair, or both.
The narrator is so pathetic and, as we suggest in his "Character Analysis," is probably physically ill. He seems to have had a pretty bad life, which probably only gets worse after the murder and subsequent confession.
Poe wrote that "melancholy is […] the most legitimate of all the poetical tones" (source). The extent to which this tone of sadness manifests in Poe's work varies widely from piece to piece. The tone of Poe's poem "The Raven" is overtly sad. The narrator's speech is rolling and mournful, echoing the feeling of sadness.
"Tell-Tale" is much different. The sadness is woven in the nervousness we find in every line. This story might not seem sad at all on the first read. We are somewhat amused by the narrator's ridiculous arguments and think the whole thing might be a sick joke. Perhaps we feel slightly superior as we unravel all the discrepancies. But, upon reflection, we realize we've read the story of a man who, plagued by diseases of the body of the mind, is in a near constant state of stress, nerves, and meltdown.
Even if he is a murderer, the narrator is a sad figure, and it comes through in the nervous, frantic tone of the story.