The setting of this spine-chilling short story is certainly key to the mood of horror and disbelief. It is perhaps important to give ourselves some context as to the kind of literature that Poe wrote before answering your question. Poe was known as a "Dark Romantic", which means he was one of a group of authors who focussed their work on the dark side of humanity - evil, sin and the capacity within us all to do terrible things. In this response I will focus on the catacombs but also how they function as a psychological symbol for the state of mind of the narrator.
Clearly, understanding Dark Romanticism becomes useful when analysing the story. We are introduced to a narrator, who, we go on to suspect, is unreliable, in that we begin to doubt what he professes to us. Consider how the story begins:
The thousand injuries of Fortunato I had borne as best I could; but when he ventured upon insult, I vowed revenge.
We begin to wonder about the accuracy of the narrator's perception when we see the trust that Fortunato displays to Montresor - if he had indeed, "ventured upon insult", he might not have been so quick to fall in to Montresor's trap.
It is clear that we are seeing the narrator beneath his mask of public respectability. The setting of the story is key in this respect too - it is set during carnaval, when characters wore masks and fine clothing. It is perhaps ironic that Montresor chooses this time to reveal his true inner self.
Note too, the symbolic function of the catacombs. Consider how they are described:
We had passed through walls of piled bones, with casks and puncheons intermingling, into the inmost recesses of the catacombs.
As Montresor leads Fortunato on into the ever-deeper depths of the labyrinthine catacombs, we as readers are treated to a special voyage into the psychological state of Montresor - the deeper we get, the more devilish, sadistic and horrific his thinking and actions become. It is key that Montresor commits his heinous crime once they have penetrated the depths of the catacombs and reached the finish - he is able to express his psychologically disturbed state to the extreme. Yet, I wonder whether the bricking-in of Fortunato represents the psychological repression of Montresor's evil desires and actions - we can only assume that after chillingly sealing in Fortunato and leaving him there to die, Montresor is able to put on his mask of respectability and operate in Venetian society once more. Having "buried" his unacceptable psychological side he can freely partake of "normal" society again. This, to me, is what the labyrinthine catacombs represent, contributing of course to the mood of terror and horror.