While Boston was up big late in the fourth quarter of Game 3 of the NBA Finals at TD Garden, their fans let Draymond Green have it -- chanting "F*** You" over and over again at the star after the Golden State forward had ruffled feathers in Games 1 and 2 of the series.

In fact, the shouts were so loud, the game's announcer, Mike Breen, had to mention it on the broadcast ... saying, "And Draymond Green hearing it from the crowd with an obscene chant,"

After the game, Klay was asked about it all -- and he made it clear, he wasn't a fan of Cs supporters.

"We've played in front of rude people before," Thompson said. "Dropping F-bombs with children in the crowd. Real classy. Good job, Boston."

Dubs head coach Steve Kerr also chided the Celtics fans for the chant ... adding in his postgame news conference, "Classy. Very classy."

Green himself actually didn't seem to have an issue with it -- he told media members he expected it -- and, in fact, he himself dropped a cuss word in his presser while his son sat next to him.

As for Green's wife, she clearly didn't love it ... calling the chants "disgusting" in a lengthy social media post following the Warriors' 116-100 loss in Boston.

"My kids were at the game tonight hearing that mess!" she said, before adding, "Just shameful!"

Tip-off for Game 4 of the series is slated for Friday ... will the Warriors' vocal issues with fans stop the chants then?