An unintentional response to Gen X's use of sarcasm, a post-ironic comment is one which the speaker actually says what they feel, but with a sarcastic tone. A post-ironic comment is usually accompanied with a wink or some other motion to make the listener feel that the speaker is joking, even though they're not.
Dan and Judy are laughing.
Judy looks at the clock and says, "Oh, I'm so sorry, Dan. I have to run, I forgot that I'm meeting up with Toby right now."
Dan says, "That's not cool. I'll never look at you the same," and laughs.
Judy asks, "Were you being post-ironic?"
Dan says, "Of course not," and laughs again.