Montresor shows no remorse whatsoever for his actions. When taking Fortunado down into the vaults, he explains his family's motto "Nemo me impune lacessit" to him. This translates to "No one assails me without impunity." Because Fortunado insulted him in the past, Montresor will make sure that he gets his revenge. So, the fact that he considers it an act of justice just fulfills his family motto.
Poes' stories were always quite chilling. He wrote stories of horror naturally and often. He did this for the purpose that all writers write--he did it to entertain. The fact that Poe convincingly portrays his main characters, and does so in the first person, proves that he wants the reader to believe that he shares his characters' feelings. This makes the story even more gruesome and hard to believe. Using a character like Montresor, who states at the end of the story "For half of a century no mortal has disturbed them" (referring to Fortunado's bones), proves to the reader that Poe wants the reader to see the evil in Montresor. He kept his secret for 50 years, and yet he still feels no remorse for his actions. He only feels justice. That makes the reader wonder if he truly supported such actions in real life. This in turn makes the story even that more chilling and effective.