McCullers told reporters Kelly's actions were "unprofessional" and intentional.
"Joe Kelly threw a ball behind Bregman's head on 3-0 on purpose," McCullers said. "Not only did he take it upon himself to send a message, but he wasn't even a part of that team. We knew coming into the game he likes to go off-script. What he did was unprofessional."
There were multiple incidents involving Kelly during the sixth inning on Tuesday night. He threw a 96-mph fastball over the head of Bregman on a 3-0 count with one out.
Three batters later, Kelly threw two pitches that brushed Carlos Correa off the plate before getting the Astros shortstop to strike out on a breaking ball in the dirt. The Dodgers reliever made a pouty face and was talking to Correa while walking to the dugout.
Both benches cleared, though no punches were thrown by either side.
Astros manager Dusty Baker told reporters after the game he wasn't happy with Kelly:
"When you throw a 3-0 fastball over a guy's head, now you're flirting with ending his career. And a couple of other balls were close. And then what really enraged everybody is when he told Carlos … he struck him out and he told him, 'Nice swing, b---h.' What are you supposed to do with that? What upset me is the umpire warned us. Why don't you warn him? He's the one throwing the ball and he's the one who started this mess in the first place. I don't like it at all."
After MLB disciplined the Astros for cheating during the 2017 season, when they defeated the Dodgers in the World Series, and part of the 2018 season, several Los Angeles players expressed their anger at potentially losing a title because its opponent was breaking the rules.
"It's hard to feel like they earned it," Justin Turner told reporters in January. "Just not 100 percent sure if they should be called champions for the rest of their lives."
Kelly is in his second season with the Dodgers after signing a three-year contract with the team in Dec. 2018.