I'm going to go out on a limb here and say that "I was joking" would probably be the most natural way.
I vaguely remember having this conversation years ago and I think the end result is that there are certain types of American humor that Koreans just don't get (and vice versa, of course).
Kind of how most british comedy isn't that funny to americans. Brits will say its just more subtle, and we will say its just not that funny. now suppose for a second that brits and americans spoke 2 different languages (no jokes, please!). How would a british person say to an american that it was their "subtle british humor"... there wouldn't be a word for it in English, a word for that type of humor because it is foreign to us. The most direct way would be to say "that was a joke" and the listener ends up assuming that obviously their sense of humor is different.
I'm sort of babbling here, but I guess what I'm trying to say is that over the years (because I am old and wise, but mostly just old) I've decided that sometimes its better to say something in a way that makes to most sense to the listener, even if its not exactly what you are trying to say. So that they get 90% of what you were trying to say even if some of the nuance is lost.
But if you really wanted to explain the lighter side of sarcasm, well, thats far beyond my speaking level
