The ejection was Boone's fourth of 2019, according to Baseball Reference.
As Boone was leaving, the umpires' attention turned to outfielder Brett Gardner. He was eventually tossed for banging his bat against the roof of the dugout - a routine he's adopted in recent weeks.
"Maybe I can use something else to hit something else," Gardner said after Saturday's contest, according to SNY's Yankees Videos. "Maybe I can take the helmet to the helmet rack and that's not as loud and that'll be okay."
Gardner was heaved from an Aug. 9 game against the Toronto Blue Jays after similarly striking the dugout ceiling.
"I feel like I kind of had a target on my back after Boone got ejected, which we were all fired up about when your manager stands up for you in that way," he continued. "I felt like as soon as I hit the top of the dugout, (umpire) Phil (Cuzzi) was running over from first base pointing in the dugout telling me I can't do that and threw me out.
"I asked him why and nobody's told me that I can't do that, nobody's told me that I can't make noise. I didn't direct anything at anyone, didn't say anything."
Gardner added he expects to have a conversation with MLB chief baseball officer Joe Torre about the ejection.
"It got taken too far with sending Gardy out of the game," Boone said postgame, according to SNY's Yankees Videos. "We're playing for a lot right now and you can feel that with all our guys ... We're playing for keeps.
Asked about Gardner hitting the dugout ceiling with his bat again, Boone added: "We'll work closely with the commissioner's office and find out what's acceptable and not and try and be respectful of that and do a better job of staying in the game."
Yankees left-hander CC Sabathia was also ejected from the contest.