Coburn and his wife, Carolyn, hoped to undo any damage inflicted by his previous interviews, saying he wanted to "apologize to everyone associated with Tonalist" and "all the horse racing in the world."
"Very ashamed of myself," Steve Coburn told GMA. "Very ashamed. I need to apologize to a lot of people."
California Chrome, which had won the Kentucky Derby and Preakness Stakes and had hoped to become the first Triple Crown winner in 36 years, finished in a dead heat for fourth with Wicked Strong in Saturday's race.
"It's just the emotion of the whole journey coming together at one time," the 61-year-old Coburn said Monday.
Added Carolyn Coburn: "I'm proud of him for coming up here and doing this. It was something we needed to do. Our story has given so much joy to so many people. I hope that this 30 seconds doesn't destroy all that."
Tonalist had not competed in the Kentucky Derby or the Preakness Stakes, which drew Coburn's ire in an interview immediately after the Belmont race with NBC and subsequent interviews with other media outlets, including ESPN.
"It says Triple Crown. You nominate your horse for the Triple Crown. That means three," Coburn said in the trackside interview with ESPN on Sunday. "Even the Triple Crown trophy has three points on it. So when you earn enough points to run in the Kentucky Derby, those 20 horses that start in the Kentucky Derby should be the only 20 allowed to run in the Preakness and the Belmont for the Triple Crown."
He also made a questionable analogy of why Tonalist's participation Saturday was unfair.
"These people nominate their horses for the Triple Crown, and then they hold out two [races] and then come back and run one," Coburn told ESPN. "That would be like me at 6-2 playing basketball with a kid in a wheelchair. They haven't done anything with their horses in the Triple Crown. There were three horses in this race that ran in the first two -- California Chrome, Ride on Curlin and General a Rod. None of the other horses did. You figure out. You ask yourself, 'Would it be fair if I played basketball with a child in a wheelchair?'"
On Monday, Coburn was apologetic to Tonalist and the horse's backers.
"I need to apologize to the winners. They run a beautiful race. They deserve that. I didn't mean to take anything away from them," Coburn said. "... Congratulations, you got a fantastic horse. He deserved to win. He won the race, fair and square."
The Associated Press contributed to this report.
Coburn Apologizes For 'Shameful' Rant
California Chrome co-owner Steve Coburn apologizes to Belmont Stakes winner Tonalist for his rant after California Chrome fell short of the Triple Crown.
California Chrome's Owner Rants About System
Steve Coburn, the co-owner of California Chrome, expresses his displeasure with the Triple Crown rules for allowing "cheaters" to race in only the Belmont Stakes.
Trainer Nick Zito On Coburn's Triple Crown Rant
Hall of Fame horse trainer Nick Zito weighs in on California Chrome co-owner Steve Coburn's criticism of the Triple Crown process.
No Triple Crown
Victor Espinoza, California Chrome's jockey, came up short at the Belmont Stakes, failing to win the Triple Crown.