Rockets Coach Kevin McHale said Barnes crossed the line by making the comment.
"You don't say anything to anybody's mom," McHale, a known trash-talker when he played for the Boston Celtics in the 1980s, said Thursday. "If you have something to say, say it to the guy you're playing against.
"I came from an era where everybody talked smack and there was a lot of stuff going on. But not like that. It was much more 'I'm going to kick your [butt]. What're you going to say about that?' It went from there."
Clippers Coach Doc Rivers said he was made aware of Barnes' comments Thursday morning.
Rivers talked about his personal rules for engaging in trash-talking.
"I don't think you should, unless you're doing it for fun, to have fun," Rivers said in a conference call with reporters. "I found the fans in Houston to be pretty much fun. They're loud, they get on you, but in a nice way. So I think as long as you keep it that way, it's good."
McHale recalled how he used to talk trash to Magic Johnson when the Celtics and Lakers faced each other.
But McHale said he never brought up Johnson’s mother in the conversation.
“I never thought about talking bad about Magic’s mother,” McHale said. “It was hard enough talking [trash] to Magic. We all talked smack, but nothing like that. My goodness! That thought never even crossed your mind.”
Willis told TMZ.com: "What he told me was that he would never want to disrespect anyone's mother because his mother passed from cancer ... and that he was sorry.
"I accept his apology."