The Oakland Athletics starter, who got into it with Rodriguez after A-Rod ran across the mound following an out in the April 22 game in Oakland, said he may want to throw fists the next time. The Yankees next face the Athletics July 5-7, again in Oakland.
"There are things that are going to have to happen," Braden told CSN Bay Area on Wednesday. "Out of respect to my teammates, out of respect to the game. I think he's probably garnered a new respect for the unwritten rules and the people who hold them close to their game. But I think you're right, we don't do much talking in the 209."
The 209 is a reference to Stockton, Calif., where Braden is from and attended high school.
Rodriguez, speaking before Friday night's game at Boston, tried to avoid extending the controversy, but he couldn't shy away from taking a slight shot after being asked by a reporter if he thought Braden would throw at him when the teams meet in July.
"I think Major League Baseball reads the same articles as we do," Rodriguez said. "Now, look, I really don't want to extend his extra 15 minutes of fame."
Otherwise, Rodriguez tried to stay clear of going back and forth.
"Look, it is tempting to sit back here and go back and forth with the media for the next three months, but I'm not going to do that," said Rodriguez, who reiterated some form of that answer over the less-than-five-minute interview session.
Braden said he was particularly peeved that Rodriguez had initially dismissed his actions and words merely because Braden hasn't done much as a major leaguer yet.
"There's two ways that I can comment on that, and I'll give you both of them," Braden said to CSN Bay Area. "One, I was always told if you give a fool enough rope, he'll hang himself, and with those comments, he had all the rope he needed. No. 2, I didn't know there was a criteria in order to compete against A-Rod."
Rodriguez also is a selfish player, Braden added.
"He's an individualistic player," Braden told CSN Bay Area. "He plays for the name on the back of the jersey, not the front. I don't know if he's noticed, but he doesn't have a name on the back over there so he should play for the name on the front."
There was never a clear-cut decision on whether Rodriguez actually violated any unwritten rule of baseball, and a day after the game, A-Rod still didn't see the issue.
"I was tired," he said. "It's really not that big of a deal. I've done that maybe a few dozen times. It's the shortest route. As I said yesterday, I thought it was pretty funny."
Braden certainly didn't.
He shouted at Rodriguez after the inning ended, then continued his rant postgame, saying how disappointed he was with the Yankees slugger.
Andrew Marchand covers baseball for ESPNNewYork.com. Information from The Associated Press was used in this report.