"Crazy stuff like that happens," Barnes said.
Barnes hit a grand slam and a three-run shot while teammate Justin Turner hit a two-run homer as the Dodgers finished June with 53 home runs, a franchise record for any month.
But the talk afterward centered on Dodgers pitcher Alex Wood threatening "to drill" Padres baserunner Jose Pirela and an ensuing altercation between Dodgers manager Dave Roberts and counterpart Andy Green that led to Roberts shoving Green.
Both managers were ejected.
"I probably got too emotional," said Roberts, who could face punishment from the commissioner's office for also bumping crew chief Sam Holbrook when he charged Green.
Roberts said he was sticking up for Wood in response to Green making a derogatory remark about the pitcher.
Wood, who went six innings with one run allowed, improved his record to 9-0 and lowered his ERA to 1.83 -- but not before screaming a threat at Pirela in the first inning.
Plate umpire Greg Gibson said second-base umpire D.J. Reyburn heard Wood threaten Pirela, who was at second base.
"He said, 'If you keep giving away location, I'm going to drill you,'" Gibson said. "I went to the mound to change balls out. I've known Alex for a while. I said, 'Alex, what's going on?' He said, 'If he gives away the signs again, I'm going to drill him.' Right then, my hands are tied."
Gibson issued a warning to both managers but opted to defer a full explanation because he wanted to keep the game moving.
Wood said he believed Pirela was gesturing to Padres hitters the setup location of Barnes.
"I was seeing red," Wood said. "Things are said that nobody probably means."
When Gibson summoned Roberts and Green for an explanation before the second inning, the managers got into an argument.
Roberts broke away from Gibson and knocked Green back a step while contacting Holbrook in the back.
"I probably could have handled it a little differently," Roberts said.
Roberts said he considers it part of the game when a baserunner "gives location" to a hitter.
He shared that opinion with Wood, he said. But he said he "didn't appreciate" Green's comments about the pitcher.
"The number one thing I took issue with was the threat on the mound from their pitcher to our player, that he was going to drill him," Green said. "It's unacceptable."
The Padres manager didn't approve of Gibson's response to Wood's threat.
"I understand what the umpiring crew was trying to do by issuing warnings, but to me, if you're making threats to hit a guy on the baseball field, that's an ejection right there, and they didn't choose to handle it that way," Green said.
Barnes gave the Dodgers a 4-0 lead with a two-out drive beyond the left-field wall off Clayton Richard (5-8) in the first. Homering twice in a game for the first time, Barnes made it 10-1 with his fourth, off Jose Valdez in the sixth.
Logan Forsythe had four hits and a walk for the Dodgers, who are 6-1 against San Diego this season.
L.A's 54-28 record leads the National League West.