James Corden Rolling Stones Snubbed My 'Karaoke'? That's News To Me

11/7/2016 6:39 AM PST

James Corden isn't always the jolly host he plays on TV ... and that's probably 'cause he can't always get the guests he wants for his sing-along shtick. 

We got James leaving Craig's Sunday where he got short and defensive when asked what songs he would have sung with The Rolling Stones for "Carpool Karaoke" -- assuming the rumors he got snubbed by them are true.

Watch -- he has another question on his mind entirely ... and a bitchy answer too.