The incident occurred Thursday at the Staples Center with 3:14 remaining in the Clippers' 126-107 loss to the Utah Jazz.
Rivers told a fan to "shut the (expletive) up" during the game.
"I definitely shouldn't have said anything," Rivers said before Friday's practice in Dallas. "This is the message I want to say. This is the message I want to say. I'm sorry for using profanity, but I was sticking up for my teammate, bottom line."