The pair shoved each other, and Cousins even appeared to direct an elbow Griffin's way in the Clippers' 93-85 win.
But Griffin told reporters after the game that he was going to leave what happened between the two players on the court and not discuss it with the media.
Informed of Griffin's comments afterward, the second-year Kings player took issue.
"Of course that's what Blake is going to say because he's in L.A., where actors belong," Cousins told reporters in Sacramento. "He's an actor, so of course he would say that."
Cousins fouled out in only 18 minutes of play, finishing with just eight points and three rebounds. Griffin was whistled only three times in 38 minutes and finished with 14 points and nine rebounds.
"If they're going to let it be physical, it's usually physical on both ends," Cousins said. "You saw the game, so I don't really have to say much."
Asked about the fifth foul he received for a play on Griffin with a little more than a minute left in the game, Cousins indicated he believed Griffin was faking.
"I guess the wind from my hand hit him in the eye and I guess he got fouled by the wind," Cousins said. "I'm not sure."
The NBA announced on Friday that Cousins is being fined $25,000 for his public criticism of officials.
The Kings and Clippers play again Saturday night in Los Angeles, the only home-and-home the Clippers have this season.