This is a story that is all about the psychological process of facing your own death and the kind of thoughts and emotions that go through your mind at such a time. The narrator and his two friends are due to face the firing squad the next day, and we are privileged observers of what goes on in the narrator's mind and what he observes happening with his two friends. As such, this story is about ultimate realities and how we can face them to the best of our ability.
The quote you have selected is very pertinent when we bear this in mind. Let us just remind ourselves of the meaning of the word "counterfeit." In this context, counterfeit means to carry on a deception or to dissemble. This refers to one possible psychological reaction that man can have when faced with death. The narrator here expresses that he has spend his time trying to trick or deceive eternity or death. However, at this stage in this excellent short story, he realises how in vain that attempt was and how he now must face eternity head on without any more attempts to avoid or get away from death. This quote therefore represents an acceptance of the narrator's fate.