The five-year-old pulled up lame the second time round the track in Australia and vets euphanised the animal.
Mr O’Brien said: “Unfortunately these things can happen to a horse galloping around the field at home.
“It’s very sad. It could have been worse, (jockey) Ryan (Moore) could have taken a fall off him, someone could have been seriously injured.”
But animal groups were left furious over the death in the race which was won Cross Counter.
The RSPCA said the tragedy “highlights the very real risks to horses from racing.”
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And Peta Australia, which said 119 horses had died in Australia races between August 2017 and July 2018 called for an investigation.
A spokesperson said the public holiday for the race should be replaced with a day “more in line with animal loving Australians values.”
Before the race, a spokeswoman warned people not to ‘gamble with horses lives’.
Spokeswoman Emily Rice told Australia’s SBS News: “We are seeing the more people are educated on what the problem is, the more people make up their own decision to not participate in Melbourne Cup sweeps and events.
“I think there is beginning to be a lot more knowledge about the fact, ‘you bet, they die’. If people don’t place bets on these horses, which is literally gambling with their lives, these horses aren’t flogged into an early grave.
“We are seeing more workplaces decide they are not going to formally acknowledge the Cup is on and we are seeing more people decide not to go to the race courses.”
There was also an outcry on Twitter, which one social media user writing: “The Melbourne Cup just ran and one of the horses was injured badly… i hope they’re ok, I feel sick to my stomach.”
The Coalition for the Protection of Racehorses followed suit in a Facebook post. “As only a five-year-old, [The Cliffsofmoher] had won $1.7 million for his owners. Today he broke his shoulder in the Melbourne Cup and was killed on the track,” the post read.
“No horse deserves to die for gambling profits, but it happens every three days, and we are so sorry.”
In a statement, RSPCA Australia spokesperson Jane Speechley said: “Our thoughts are with animal lovers across the country who have been affected by this loss, and confronted by the very real risks posed by racing to the horses involved.
“RSPCA Australia has long voiced its concerns about the welfare of racehorses, including the use of inhumane devices such as whips and tongue ties, as well as the risk to injury and death during races.
“Today’s tragedy is a stark reminder of the risks these horses face every time they run, and highlights that behind the gloss and glamour of Cup celebrations there is a dark reality.”
There have been four horse deaths in the race since 2014.
In 2013, French mare Verena broke down in the back straight and died and the following year the Melbourne Cup was stunned when two more horses died.
The 2014 favourite Admire Rakti collapsed of a suspected heart attack five minutes after the race finished and died in his stable while Arnaldo broke his right hind leg and was euthanised.
In 2015 Red Cadeaux, a British Thoroughbred who had finished runner up in 2011, 2013 and 2014, was euthanised following complications in surgery for an injury sustained in the race.
Last year Regal Monarch had to be euthanised after breaking his right leg in the race.