Poe, the master of creepy stories about creepy people, in the setting of this story, found what is perhaps the creepiest possible setting. They are in dark, mazey, damp, rat and insect-infected tombs. It doesn't get more eerie than that. Ironically, the setting isn't for a sudden zombie-uprising, as modern Hollywood might make it today, but rather the setting for the twisted plans of Montresor to commit his premeditated act of revenge. One can easily imagine his success in this setting, and sense the feeling of doom and despair. The setting can also represent Montresor's mind, which is full of ill-intent, death, and revenge to be buried forever.
The setting itself works against the unfortunate Fortunado, as an antagonist: The damp and cold impacts his cough, the narrow and winding passageway disorients him, and the depth of their penetration into the old catacombs ensures he won't be discovered in his tomb. In this way, the setting aids and abets Montresor in his crime, and becomes a supplementary force for evil in the story.
Poe is known for his settings. This setting creates a very suspenseful scene for this story. The use of the deep and cold catacombs lures the reader in to wonder what will happen next. Then the use of verbal irony with Montressor creates fear for the reader. He claims (very unconvincingly) that he is concerned for Fortunado's cold. He doesn't "want him to die from a cough." However, he wants him to die. We know this as the reader, and Montressor's personality is clear from the beginning. He wants revenge, and the fact that we don't know where they are going creates even more apprehension. The depths they travel into his family's crypt is equally unnerving. We know the further they get from people, the more dangerous it is for the all unassuming Fortunado. That creates more evil in Montressor as well. We see him as paying Fortunado back for the insults that were given to him. And his premeditation of making sure the servants were gone and having the bricks and materials needed in the base of the catacombs all points to the development of the character Montressor.