One example is when the narrator is describing the catacombs beneath his palazzo. He says, "I will not deny that there is much of the horrible in these vaults, but then in catacombs there is much which only the ghoul may appreciate. The blackness of darkness, and the odor of the damp earth, the vaults and the arches, the decayed mold, and the dripping wet, the rats, the fungus-growing walls, the cobwebs, the skeleton, the blackness, all these must afford a delight which I cannot enjoy. I would not have you to suppose, however, that my chambers are without their attractions." This passage is significant because the narrator is describing a very dark and unpleasant place. However, he is careful not to say too much about it, as if he is afraid of revealing something about himself.
Another example is when the narrator is talking about his relationship with Fortunato. He says, "He had a weak point -- this Fortunato -- although in other regards he was a man to be respected and even feared. He prided himself on his connoisseurship in wine. Few Italians have the true virtuoso spirit. For the most part their enthusiasm is adopted to suit the time and opportunity, to practice imposture upon the British and Austrian millionaires. In painting and gemmary Fortunato, like his countrymen, was a quack, but in the matter of old wines he was sincere. In this respect I did not differ from him materially; I was skillful in the Italian vintages myself, not less a connoisseur than he." This passage is significant because the narrator is talking about his own strengths and weaknesses. However, he is careful not to reveal too much about himself, as if he is afraid of being judged.
Overall, the narrator of "The Cask of Amontillado" is somewhat cautious about not revealing too much about himself. This is evident in the way that he describes the catacombs and his relationship with Fortunato. He is careful not to say too much about these things, as if he is afraid of revealing something about himself.