Kennedy hit Los Angeles rookie Yasiel Puig and pitcher Zack Greinke with high pitches Tuesday night, and a day later the Dodgers were still taking exception to where they were thrown.
"Anything like that is going to leave a lot of taste in people's mouths," manager Don Mattingly said.
Mattingly said he doesn't think Kennedy hit Puig deliberately. The ball deflected off the young slugger's shoulder and grazed his nose.
The pitch from Kennedy to Greinke deflected off his helmet and struck his upper left shoulder.
"The second ball is no doubt intentional," Mattingly said. "That's two balls thrown last night that could have ended guys' careers."
Arizona manager Kirk Gibson repeated his earlier denial that Kennedy was head-hunting Greinke.
"That's not our intent," he said.
The teams met in the series finale on Wednesday night, one night after their nasty fight led to six ejections, including Kennedy, Puig and Gibson.
"We had some guys on our team get heated and overreacted," Dodgers ace Clayton Kershaw said.
Arizona catcher Miguel Montero had a different view.
"We both went at it, and it was kind of fun," he said.
No discipline by Major League Baseball was expected to be announced until at least Thursday. Both teams are off that day. The Dodgers open a nine-game road trip in Pittsburgh on Friday, while the Diamondbacks play the first of three games at San Diego.
The teams meet again in Arizona for three games from July 8-10.
In an amusing bit of timing, MLB announced Wednesday that the Diamondbacks and Dodgers will open the 2014 season against each other with a two-game series in Australia.
The fight was the second ugly one the Dodgers have been involved in this season. Greinke spent more than a month on the disabled list after breaking his collarbone in a brawl with Carlos Quentin after hitting the Padres outfielder with a pitch on April 11.
Puig was scratched Wednesday night with a strained right shoulder, although the Dodgers didn't immediately explain how he was hurt. He was a fiery presence in the fight, yelling and engaging in the scrum that nearly carried over to the stands.
"One thing we've learned from Yasiel is there's no half-speed," Mattingly said. "It's fast, hard and all the time, so I'm really not surprised."
Puig came into the game batting .500 just 1 1/2 weeks into his major league career.
"The only way you can get the kid out right now is to throw him inside, and that's how we got him out the first two times up," Arizona infielder Willie Bloomquist said. "To say we were trying to hit him, that's crazy. We're certainly not trying to hit a kid in the face."
Gibson agreed, saying, "We found a little hole up and in. Ian's trying to go back in there and the ball got away. You never, ever want to try and hit anybody close to the eye."
Also getting in their licks were several coaches who dominated baseball as players in the 1980s and '90s.
Gibson and Dodgers hitting coach Mark McGwire clutched each other's tops and went nose-to-nose. McGwire also squared off in a tense standoff with Diamondbacks third base coach Matt Williams
"It was a good one, huh? These guys are tough," said Montero, who got hit in the back by a pitch from Greinke. "Those coaches are tough. Old-school right there, I guess. There's a lot of power there."
Don Baylor, Mattingly's former New York Yankees teammate and currently Arizona's hitting coach, held his ground among a surge of Dodgers. Mattingly wrestled with Arizona bench coach Alan Trammell as he tried to get at Gibson. Williams had Mattingly in a not-so-friendly bear hug at one point.
"I don't get like that very often," Mattingly said. "I didn't really know that was Tram. I had someone on me. If I see Tram out there (before the game) I would definitely apologize. I like Tram a lot."
Baylor, Williams and Trammell declined to talk to reporters Wednesday.
Mattingly and Kershaw thought the beaning should have stopped after Puig and Montero got hit, with each team having struck someone. Five players in all were hit, including Arizona's Cody Ross and Mark Ellis of the Dodgers.
"Do I think Kennedy hit Puig on purpose? No," Kershaw said, "but the fact that he's a professional pitcher and he's throwing at faces. Then to do it again in Zack's face, there's no place for that. If you can't throw inside, don't go there."
Mattingly said that under baseball's unwritten code, Greinke had to retaliate after Puig was hit.
"If our guy gets hit and he doesn't protect him, then he loses respect in the clubhouse and that's not a good thing," the manager said.