The crypt is important, of course. It's creepy and should make us think about both death and excess. However the carnival in Italy matters too. Everyone is in costume, they are drunk and having a good time, so their guard is down.
The setting is also used to enhance the ironic elements of the story. While there is revelry and fun on the surface, below it all is revenge and death. The Carnival atmosphere, as mentioned above, is an excellent "cover" for the dark deeds below the surface.
What is fascinating to note is how the physical journey of Fortunato and the narrator into the catacombs - delving beneath the city, every deeper - is symbolic of the journey into the interior of the narrator's psyche, for the deeper they go, the more is revealed of how disturbing the internal thoughts of the narrator are. This is what makes the setting so profoundly upsetting.
Poe's "The Cask of Amontillado" is a gothic tale: The narrator is obviously disturbed as he begins by ranting about "the thousand injuries" that he has endured by Fortunato. Of course, the entire story is narrated by this unreliable narrator that leaves the reader with some trepidation him/herself. The catacombs are foreboding, damp and dark with the bones of his ancestors "lying promiscuously" about. Montesor's repetition of how narrow, how wet, how poor the air is in them contributes to the eeriness, as well. The perverse humor of waving the trowel and exclaiming that he, too, is a "mason" is another contribution to the gothic atmosphere. And, then, there is the less-than-charming Montesor coat of arms with the huge golden foot crushing a serpent. The aura of potential evil abounds.
The setting of the carnival season also serves to further Fortunato's death. Because of the festivities going on, Montresor is able to send off his servants without suspicion. He also finds Fortunato is a more malleable mood on the night that the narrator invites him over. Fortunato's jester costume represents not only the festive atmosphere outside the house, but it also eerily suggests Montresor's plans to make a fool out of his enemy.
The setting in the story is dark and spooky, and it becomes even more forbidding. As sober Montresor leads drunken Fortunato deeper and deeper into the catacombs, the implication is that only one of them is coming out, and it won't be Fortunato. The setting itself is a place of death. This is a place where people are buried, where their bones lie undisturbed for centuries.