Bradley endured a chastening first two days in the American hotseat as the US slipped to a record 11.5-4.5 deficit which left a European victory looking like a formality.
But his side turned up on Sunday and threatened the greatest recovery in Ryder Cup history, winning eight and a half points from 12 singles matches.
Europe just got over the line to claim a historic 15-13 victory at Bethpage Black in New York.
"The Europeans won one match today. You think about the odds of something like that happening, just on a coin flip would be incredible," Bradley said.
"When you go out in sports and you're battling your butt off to win, it just shows you just how proud these guys are and how much they want this and how much this means to them.
"To go out there today and do what they did is close to a miracle."
Bradley said the ultimate loss was "no one's fault but mine".
"When you are the leader of the team and you're the coach, the captain, whatever you want to call it, and you lose, you have to take the blame," he said.
"Sometimes in sports, you go up against an opponent that sometimes beats you; they play better.
"And they played better than us. We gave it a great fight, that's for sure."
Bradley had faced a lot of criticism, especially for some of his foursomes and fourballs pairings, while the set up of the course, with wide fairways, light rough and soft greens, also appeared to suit the Europeans.
"We tried to set the course up to help our team," Bradley added. "Obviously it wasn't the right decision.
"I definitely made a mistake on the course set-up. I should have listened a little bit more to my intuition.
"But the Europeans played just incredible golf. Doesn't matter how you set the course up when you play that well."
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