Girardi said his profane rant at O'Nora probably was the angriest he's been on a ball field.
Rodriguez was suspended for 211 games on Aug. 5 for violating baseball's drug and labor agreements but is playing while he appeals. Red Sox pitcher John Lackey criticized the rules last week for allowing A-Rod to play.
Girardi said prior to the announcement that if Dempster wasn't punished, it would make Rodriguez "open season for people, and that can't happen. It's not fair. If a player is suspended for throwing at someone, they're going to get their appeal. Are we just going to throw that out, too?"
Asked later if the level of penalty would make it open season, he responded: "That's my concern. We'll find out. I sure hope not."
"If you suspend a position player three games, he misses three games," Girardi added. "You can suspend a pitcher five games, even six games and he may not miss a start. The off days come into play."
The Red Sox did not criticize the decision, saying their focus was on winning games and making it to the playoffs.
"We fully respect what MLB has decided to do and hand down the suspension," manager John Farrell said. "Never has it been uttered that it's been unjust. To Ryan's credit, he's serving the suspension starting tonight."
New York didn't retaliate Sunday. Girardi wouldn't say whether there is a need to respond when the teams next meet, at Yankee Stadium on Sept. 5.
Girardi said "protecting your own" in baseball has gone on for "for a long time. And unfortunately you're part of those situations sometimes, but that's part of the game."
The manager also discussed the matter with his 6-year-old son, Dante.
"Part of pitching is pitching inside, that's all part of it," he recalled telling the boy. "But I don't ever want you to hit anyone on purpose."
After Sunday's game, Rodriguez declined to say whether Dempster should be suspended.
"I'm the wrong guy to be asking about suspensions. Holy mackerel," A-Rod said with a laugh. "I've got an attorney I can recommend."
AP Sports Writers Ronald Blum and Howie Rumberg in New York contributed to this report.