SAN FRANCISCO (AP) — Boston’s Ryan Dempster accepted his punishment without admitting any misdeed.

Dempster was suspended for five games and fined by Major League Baseball on Tuesday for intentionally hitting New York Yankees star Alex Rodriguez with a pitch last weekend.

While Dempster still maintains he was only trying to establish the inside part of the plate and wasn’t trying to hit Rodriguez on purpose, he will not contest the punishment and began serving it Tuesday.

“I thought about appealing,” Dempster said before Boston played the Giants. “At the end of the day, I think Major League Baseball does a really good job of thinking through punishments before they hand them out. I thought it was in the best interest of us as a team to go ahead and serve my suspension.”

MLB senior vice president Joe Garagiola Jr. announced the penalty two days after Dempster hit A-Rod in the second inning at Fenway Park. Yankees manager Joe Girardi was fined for arguing with plate umpire Brian O’Nora.

Dempster’s fine was $2,500 and Girardi’s was $5,000, people familiar with the discipline told The Associated Press. They spoke on condition of anonymity because the amounts were not announced.

Dempster was scheduled to pitch Saturday at the Los Angeles Dodgers but now could be pushed back to next Tuesday’s homestand opener against Baltimore. He will throw a simulated game on Friday.

Boston is off Thursday, and Jon Lester will be able to pitch on regular rest Saturday in Dempster’s place. Jake Peavy is set to go Sunday on normal four days’ rest.

“That has nothing to do with it,” Dempster said. “I think it has to do with taking my suspension and put it past. There’s no point in carrying out an appeals process. We have other things to worry about and that’s going out and winning a ballgame tonight against the San Francisco Giants. I’ll take my punishment.”

Earlier Tuesday, Girardi insisted it would be “open season” on Rodriguez if MLB failed to suspend Dempster. Girardi had hoped for a suspension long enough to make Dempster miss a turn.

“I think I made my feelings pretty clear then,” Girardi said after the suspension was announced.

Dempster threw one pitch behind A-Rod’s knees and two more inside during the second inning. Then his 3-0 pitch struck Rodriguez’s left elbow pad and ricocheted off his back.

“You don’t throw at a guy four times,” Yankees pitcher CC Sabathia said. “He violated every code in every way.”

Dempster said he will never stop pitching inside.

“That’s a real important part of pitching to any hitter, especially a big power hitter,” he said.

Girardi sprinted onto the field, screaming at O’Nora for not ejecting the pitcher. Girardi was tossed as the benches and bullpens emptied, and Rodriguez homered off Dempster to spark a sixth-inning rally that lifted New York to a 9-6 win.

“That baseball is a weapon. It’s not a tennis ball. Or it’s not an Incrediball that’s soft. It’s a weapon, and it can do a lot of damage to someone’s life,” Girardi said before a doubleheader against Toronto. “And that’s why I was so upset about it. You can express your opinion and be upset with someone, but you just can’t start throwing baseballs at people. I mean, it’s scary.”

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.”