Before we begin to answer the question, we need to be sure that we have an understanding of the terms at play, here. First, "protagonist." This is the character in the story that has a goal that we generally support, and the character that we would like to see succeed in their ambitions. The "antagonist," on the other hand, is the character that has a goal contrary to the protagonist. He, she, or it, wants to stop the protagonist from succeeding.
So what does this mean for the story "The Pit and the Pendulum?" Let's see:
The protagonist is not identified by name. The story is written in the first person perspective, so we get a clearer idea of who the character is (mentally) than we do of who he is specifically. We don't have a clear idea of what he did to deserve it (the implication, actually, is that he didn't do anything) but he is being punished by "black-robed judges" for the unknown offense. If he did do something it was religious in nature, as implied by the final sentence of the story which mentions the inquisition.
The goal of the protagonist in the story is simply to survive the ordeal that he finds himself in. He is the protagonist because the reader wants to see him succeed. No one (at least not that I know) roots for the blade to cut the guy in half.
Now for the antagonist. In this case, because of the last line in the story, we understand that the judges are part of the inquisition. Based on the information given, that the story takes place in the city of Toledo, we can guess the year to be about 1485. The Catholic church was attempting to eradicate "heretics" through grisly means. They are the antagonists because they have a goal contrary to the protagonist (they want him to die, and he does not want to) and we do not root for them to succeed.