Irritably suggests a negative emotional state, signaling impatience, annoyance, or irritation. He irritably declined the offer, too upset to consider it.
Pro Tip 2/3
Not Rude
While being irritable isn't polite, it's less harsh than being aggressive or confrontational. She irritably asked us to be quiet, but wasn’t really rude.
Pro Tip 3/3
Intensity
Irritably often implies a mild or moderate level of irritation, not extreme anger. He answered the phone irritably, clearly bothered by the interruption.