After the contest, Cousins called Harris a "kid" and said he was "tired" of the guard.
"I don't know what his issue is, but I can definitely solve it," Cousins said.
Before Utah played Denver, Harris who rarely gives pregame interviews said he didn't want to talk about the incident because he had a game to focus on.
If Cousins tries to start anything March 30 when Utah hosts Sacramento, Watson said he'll be ready.
"The DeMarcus kid: I don't know," Watson said. "We're in the playoff hunt. I'm not sure what his purpose is. I know what our purpose is."
Inspired by his team's strong edge and Harris standing up to Cousins, Watson reflected on his time in Memphis playing for coach Hubie Brown.
"No one wanted to deal with Hubie because Hubie, he'd talk to you for 40 minutes straight and not let you get in a word. And no word would be nice or quotable. And then he'd tell you he loves you," Watson said. "It was extreme."
The 11-year veteran believes the NBA is still a physical game, despite a lack of hard fouls and most in-game jawing rarely turning into punches.
"I don't think the game is different, I just think it's reprimanded differently," Watson said. "Guys have different mentalities. Probably because it'd be like coach [Jerry] Sloan who'd chase guys on the court. Like, 'This coach is crazy.' "Brian T. Smith Twitter: @tribjazz