"He called me and said, 'Coach, this isn't right what they're about to do, but [they] are gonna let you go,'" Kidd told ESPN.
Kidd said he replied, "I had a feeling that was gonna take place."
To which Antetokounmpo responded, "'What can I do? I'll call the owners, I'll call my agent."
Kidd said he told him, "There's nothing you can do. All you can do is tell the truth. That's it."
Kidd said he thanked Antetokounmpo for his loyalty and that he was "thankful to be able to coach him and help him become the player he is today. And I know when our paths cross again, he'll be much better."
Kidd said he was officially informed he'd been fired about 15 minutes later when he met with general manager Jon Horst and team president Peter Feigin at a pizza restaurant.
Kidd said he felt the firing was "handled wrong," but that he was thankful for his time in Milwaukee.
"I enjoyed my time in Milwaukee. There's no regrets. We took an organization that was in a bad place and shined a light on it. They're still young in running their race. Giannis is young in running his new race, as one of the best players in the world."
Kidd said that when he met with team officials after 3 p.m. CT on Monday, he already knew what they were about to tell him.
"There was no explanation. It was just, 'We're going in another direction.'"
Kidd said Antetokounmpo had called him at about 2:45 p.m. CT on Monday because he was about to head to the arena for the game against Phoenix. Once he saw that call come in, he suspected something was amiss.
"That's the truth. You wanna look at my phone and see the time stamps?" Kidd said.
Kidd said he harbors no ill will toward the Bucks.
"It's a business," he said. "That's what people have to understand. People get fired, they get traded. It's a job."