The whole interaction was thankfully caught on camera because Coco and her dad/coach were mic'd up for her ASB Classic match in New Zealand ... and in between sets, he gave her a pep talk.

Her dad, Corey, is heard giving out compliments left and right ... but got a bit carried away when he said, "There's one thing you did the last 3 games, you ain't give up no free points on no damn serve. That serve is weak."

That's when Coco chastised pops for using a bad word while mic'd ... saying, "You can't curse."

Dad's reaction is priceless ... at first he can't believe he cussed on a hot mic, but then directly apologized into the microphone for the slip-up.

But then Corey, still in disbelief, asks Coco again if he really cussed ... and she tells him he did, in fact, say "the d word."

"Oh, well that don't even count," Dad responded.

Coco wasn't havin' it, though ... saying, "in some places, it does!!"

Dad apologized once again ... and Gauff went on to lose the match to Laura Siegemund.