Former Kentucky Derby and Preakness winner Chrome, with jockey Victor Espinoza, was six for six this year with £13 million career earnings to make him the richest horse in American thoroughbred history, but all good things come to an end.
"I am so proud of him, he ran a great race," said Espinoza.
"Maybe in hindsight I should have let him roll a bit earlier. We have had our ups and downs, and I know what it's like to be down and then come back.
"He was cruising, but we've probably met a good horse today."
The Khalid Abdullah-owned Arrogate gave legendary trainer Bob Baffert his third Classic victory in a row, but admitted he thought his horse would have to settle for second best.
"I thought there was no chance turning for home that he could catch Chrome -- Chrome is such a great horse. It takes a lot to get me excited and that was some race," he said.
Baffert, who trained the great American Pharoah to victory at the Classic last year and Bayern in 2014, knows he has another future great with his late maturing colt.
"This horse is just learning how to run and what a great race," he added.
Chrome's trainer, 79-year-old Art Sherman, said that his horse would likely run at least one more time, with the Pegasus World Cup Invitational at Gulfstream Park in January targeted.
He said: "I'm very proud of the way he ran and there are no excuses. What can I say, he ran his eyeballs out. This was really a great race. He will be back for sure."
Jockey Smith was extending his record haul of Breeders' Cup victories to 25 and is predicted to win many more prestigious races with Arrogate, who first showed his potential with a 13 1/4-length victory at the Travers Stakes in August.