CHICAGO -- White Sox shortstop Tim Anderson says there was no inside joke between he and New York Yankees third baseman Josh Donaldson regarding Donaldson calling Anderson "Jackie" over the weekend, in reference to Jackie Robinson.

Anderson, speaking publicly on Tuesday for the first time since Major League Baseball punished Donaldson with a one-game suspension, said the two haven't had a relationship since the first time he called him Jackie, back in 2019.

"He did say that, and I told him we never have to talk again," Anderson recalled. "I don't speak to you, you don't speak to me, if that's how you want to refer to me. I know, he knew exactly what he was doing because I already told him."

Anderson claims while Donaldson played for the Minnesota Twins, the two had no contact, but that changed after a hard slide into third base by the shortstop in a game in Chicago between the two teams. The two players had words that night and then again this past weekend in New York, leading to Donaldson calling Anderson "Jackie" once again.

Donaldson said the "Jackie" comment was in reference to a 2019 interview with Sports Illustrated in which Anderson described himself as feeling like "today's Jackie Robinson" in how he's "getting to a point where I need to change the game." Donaldson said it was a reference about which he has "joked around" with Anderson in the past.

Yankees outfielder Aaron Judge said Donaldson made "a mistake." And the league, in suspending Donaldson, felt his comment was "disrespectful and in poor judgment."

Anderson was asked if he felt the one-game suspension and fine was appropriate.

"It's out of my control, so I'm cool with whatever," Anderson said. "I could care less about the suspension."

White Sox general manager Rick Hahn was equally vague about his opinion on the punishment but was more than happy with his team's response to the incident, both on and off the field. A day after the Donaldson comment, the White Sox swept the Yankees in a doubleheader.

"Tremendously proud of the way teammates coalesced around TA this weekend," Hahn said. "The support that was shown both on the field and in the clubhouse was remarkable."

Anderson's three-run home run in Game 2 was a highlight for the All-Star shortstop. Some Yankees fans had been chanting "Jackie" during some of his at-bats that day.

"It was pretty dope for me to shut them up," he said.

Anderson said he hasn't heard from the Yankees or Donaldson, and that's just fine with him.

"I'm not looking for no friendship or relationship from that behalf," he said. "I'm going to keep playing hard and being a great teammate."

Anderson indicated he's heard from all corners of the baseball world and is appreciative of the "love and support" he has received. He was asked if he thought Donaldson at least received a message from the league after being punished.

"I hope so," Anderson said.