The 53-year-old failed to regain consciousness after being knocked to the ground. He passed away in hospital after his horse fell on him having been accidentally struck in the head with a mallet.
Carlos, whose pupils included Prince Charles, King Constantine II of Greece and Sylvester Stallone, was said to be the Queen’s favourite polo player.
As well as teaching William and Harry, he also played alongside them on a number of occasions.
He once said of the brothers, "My experience with the royal family was really something very special because they are true princes.
"I remember an anecdote from a training session in which Prince William arrived four or five minutes late for a class, and said sorry more than anyone I've ever met in my life. They are fantastic people."
Recalling the day that the Queen's grandson introduced him to Kate Middleton, he said, "Prince William told Kate, 'This person is the best polo player ever, he's a legend and he's the best, and my father thinks the same.'"
In the course of his career, dad-of-two Carlos won most of the world's major tournaments, including the US Open nine times, and the British Open ten times. He reached a ten goal handicap – the sport’s maximum – and held it for 15 years.
The freak accident that resulted in his death took place at Everglades Polo Club in Wellington, Palm Beach County, where he lived.
Another player accidentally hit his horse in the head with a polo mallet. The horse whipped round and hit Carlos' head, knocking him unconscious.
His sons Carlos Jr and Mariano, as well as his brother Memo – all professional polo players - were by his bedside when he passed away on Tuesday night.