Griffin was angry after he was whistled for his second technical of the game when he became entangled with Golden State forward Andrew Bogut in the lane and tried to pull away with 10:43 left.
"Instead of just playing straight up and playing a game, it got into something more than that, and it's unfortunate because you want to play a team head-to-head," Griffin said. "You don't want to start playing other games and playing cowardly basketball."
The Warriors trailed after three quarters but rallied for a 105-103 win over the Clippers.
"If you look at it, I didn't do anything and I got thrown out of the game," Griffin said of the run-in with Bogut. "It all boils down to they (referees) fell for it. To me, that's cowardly. That's cowardly basketball."
"Honestly, I thought we were just kicking their butts and they went to something else, to be honest," Rivers said. "But that's fine."
Warriors coach Mark Jackson chose to stay out of the fray.
"We like them. Merry Christmas," he said.