I know it's popular to say that intention doesn't matter when you hurt someone, but honestly, it feels a lot worse to me when someone hurts me out of intention than out of misunderstanding. The fact that he had to explain the insult excuses you of insulting him with intent.

Apologize to him, and assure him that it won't happen again- and make sure you don't. If he's still rude to you afterwards, that's on him.