"You can't really predict how it's going to end," said Greinke, who was fined for his role in the melee. "It could be an accidental thing that starts it over again. If something is done on accident, it could be misinterpreted. Emotions are going to be a little higher. You hope nothing happens, but people make mistakes. And people might make mistakes on purpose."
On Friday, Major League Baseball handed down eight suspensions between the two clubs resulting from the brawl, including both managers for one game. On the Dodgers' end, Skip Schumaker and J.P. Howell received two games, which they will appeal. Reliever Ronald Belisario received one game, which he will not appeal.
D-backs pitcher Ian Kennedy, who hit Greinke in the shoulder and Yasiel Puig in the nose, received a 10-game suspension, while first baseman Eric Hinske got five.
Dodgers manager Don Mattingly said he understands his suspension. Belisario did as well. Schumaker, who said he was advised not to comment on the matter while the appeal is ongoing, and Howell will try to get their two games back.
"I think it's a long shot, but who knows," said Howell, who is allowed to play during the appeal process. "I'm just going to figure it out and see if I can."
Mattingly sat out Friday's opener vs. the Pirates, as did hitting coach Mark McGwire, who was suspended for two games. Bench coach Trey Hillman managed the Dodgers on Friday.
Belisario, Howell and Mattingly all said a manager missing a night doesn't really affect the flow of a team at this point in the season. The Dodgers' manager said his team "is on autopilot anyway."
"It's pretty easy at this time of year," Howell said. "We've got a flow going. We know what's going on. Nothing changes no matter who's suspended, kind of."
In addition to the player suspensions and fines, the Dodgers' organization was fined for allowing players on the disabled list to leave the dugout, as the action violated MLB rules, regardless of the nature of their exit onto the field.
"I don't know what the fine is," Greinke said. "But they're better off coming out and paying the fine than sitting in the dugout while it's happening."
Two players who had notable roles in the brawl were not suspended --- Arizona catcher Miguel Montero and Puig, the Dodgers' rookie outfielder.
Mattingly said Kennedy's suspension was fair because he escalated the conflict. Belisario, however, blamed Montero, who wasn't involved much in the scrum, but gave Greinke a glare as he walked toward home plate before he was hit by Kennedy.
"He was the one that started that fight," Belisario said. "That's not right. ... That was Montero. He called it for sure."
Mattingly didn't see it that way.
"How do you write that into a suspension: Montero looked at him before he hit Greinke," the manager said with a laugh. "Suspended for aggressive looking. Looking at him with bad intentions."
Greinke dodged most questions because he said he simply didn't know the facts and felt the people doling out the punishments had reviewed the tape at length and had all the necessary information, while he didn't.
He said it wasn't his place to comment on the suspension of Kennedy, and that he'd rather address it with him personally than do it through the media.
"Every answer I have can be put in a way to make things wrong, you know," Greinke said. "When you're asked questions that you probably shouldn't be talking about, it's hard to answer it. Because I like telling the truth, but it's hard to talk about something that shouldn't be talked about."
Mattingly said the incident will continue to be brought up each time the D-backs and Dodgers meet --- 10 more times, to be exact, including seven in September.
Belisario added: "Everybody knows that it's not over."
Mattingly, however, said not to read too much into that comment. No one will know until July 6 in Arizona, when the two teams meet again.
Steven Petrella is an associate reporter for MLB.com.
This story was not subject to the approval of Major League Baseball or its clubs.