This is an excellent question. Let us remember that this quote comes at the very end of the story, when Montresor has shut his enemy up and it appears Fortunato has already died because Montresor is unable to provoke any response from him behind the brick wall he has just constructed. What is curious about this quote is the way that it seems to point towards the lack of self-knowledge of the narrator, who not only deceives us, but deceives himself. Let us consider the quote again:
My heart grew sick--on account of the dampness of the catacombs.
The dash that follows the proclamation that his heart grew sick is then quickly filled by a justification to explain the reason for his feeling. Yet given what Montresor has just done and the silence that emerges from Fortunato, we as readers can actually come to rather a different conclusion. As inhumane as Montresor presents himself as being, this quote strongly suggests that he does have sympathy and emotions, and that he is actually shocked by what he has done to Fortunato. However, he lacks the perception to accept what his emotions are telling him and seeks an excuse to justify what he is experiencing.