The pair were involved in a number of battles during the Kings' 99-70 win over the Bulls on Monday evening.
The 33-year-old told ESPN: "He called me a clown? I mean, I'd like to respond but clowns can't talk. So [I can] mime or [give him] some animal balloons or something. Oh man.
"That's the epitome of the pot calling the kettle black. But honestly I've never been called that before. I guess there's a first time for everything. I don't have much to say about him or that.
"I think his reputation speaks for itself. He's got a short fuse and is easily irritated so you can't really breathe on the guy without him flipping out. That kind of stuff happens, he's susceptible to that and probably will be for the rest of his career."
Dunleavy has averaged 11.1 points per game this season.