"I'm very proud of him standing up for me," Starkey, 59, told Rolling Stone.
As for what his dad said about the drama? " 'I've never liked the way that little man runs that band,' " said Starr, 84, per Starkey, seemingly referring to The Who frontman Roger Daltrey.
A rep for Daltrey did not immediately respond to PEOPLE's request for comment Thursday, June 19.
Starkey had been performing with the classic-rock band for nearly three decades when it was announced that he and The Who were parting ways in April, saying he was "very proud" of his tenure.
Days later, Pete Townshend said that Starkey was not leaving the band. "There have been some communication issues, personal and private on all sides, that needed to be dealt with, and these have been aired happily," he wrote on Instagram.
In May, the band announced Starkey was leaving again. "After many years of great work on drums from Zak the time has come for a change. A poignant time," The Who and Townshend, 80, wrote on Instagram in a shared statement. "Zak has lots of new projects in hang and I wish him the best."
Starkey then posted on his Instagram account, claiming that he was fired and asked to say he quit. "I was fired two weeks after reinstatement and asked to make a statement saying I had quit the who to pursue my other musical [endeavors]," Starkey wrote. "This would be a lie."
"I love the who and would never had quit. So I didn't make the statement," continued the drummer. "Quitting the who would also have let down the countless amazing people who stood up for me (thank you all a million times over and more) thru the weeks of mayhem of me going 'in an out an in an out an in an out like a bleedin squeezebox."
Starkey followed up with another update on his supposed firing, saying that there was miscommunication between him and Daltrey, 81. "NOISE&CONFUSION!!!! I had a great phone chat with Roger [Daltrey] at the end of last week which truly confused both of us!!!" he wrote on Instagram May 26.
"Rog said I hadn't been 'fired' ... I had been 'retired' to work on my own projects. I explained to Rog that I have just spent nearly 8 weeks at my studio in Jamaica completing these projects, that my group Mantra Of The Cosmos was releasing one single at the beginning of June and after that had run its course (usually 5/6 weeks)," he continued.
"I was completely available for the foreseeable future ... Rog said 'Oh!' and we kind of left it there - On good terms and great friends as we have always been," added Starkey. "Gotta love these guys. As my mum used to say 'The mind boggles!!!' XXX.' "
When asked by Rolling Stone whether he blamed The Who over his firing, Starkey said he didn't blame anyone.
"I don't hold any grudges. It's The Who. Weirder s--- than this has gone down. I've heard them say weirder s--- than this. It's The Who -- the maddest band there's ever been."