Inexcusably means “in a way that is too bad to excuse.” It tells you how someone acted, not just that the act was bad. “He was inexcusably rude” means the rudeness itself cannot be excused. You can put it before an adjective (“inexcusably late,” “inexcusably careless”) or after the verb (“she behaved inexcusably”). It is formal and rather heavy. In everyday speech, people more often say “unforgivably,” “there is no excuse for that,” or they simply pile on “really” plus a strong adjective. The adverb does not make the person bad in every way; it marks this one piece of behaviour as past the line.

不可原諒地