Veterinary officials check for heat and sensitivity in the legs of all equine competitors under rules set up in 2005 in part to keep riders from purposely making their horse's legs tender so they would jump more carefully.
However, the rules acknowledge that injury and infection can also produce heat.
Foster said her horse Victor had a nick in the coronary band immediately above the hoof that was "like a paper cut".
International Federation of Equestrian Sports (FEI) President Princess Haya Bint Al Hussein of Jordan emphasised that Foster's disqualification was not the result of any suspected cheating.
"I do want to be very clear with you all that there is absolutely no accusation of malpractice here," the former show jumper told a news conference held to discuss the decision.
"As a former competitor, I just totally empathise with what Tiffany is going through ... It's absolutely crushing for her to experience this in her first Olympics."
Foster shook with sobs throughout the briefing, comforted by visibly angry team captain and defending individual Olympic champion Eric Lamaze.
"I just want to say that I would never do anything to jeopardise the welfare of my horse and what happened today was obviously very disappointing and devastating to me," Foster said in a broken voice.
"I feel really bad for my team and really disappointed that this is the way my first Olympic Games are going to end."
Lamaze, whose gold medal horse Hickstead collapsed and died at a World Cup event in Verona last year, said it was time to take a hard look at the FEI's rules on hypersensitivity.
"This is a complete miscarriage of justice," he said, adding that the ruling was made without officials ever taking the horse out of his stall or jogging him around.
"This horse was exercised in the morning, jumped in the morning, was fit to compete - fit to compete. How can five people poking at a horse's coronary band declare him unfit to compete? How can they ruin someone's Olympic dream?" he said.
"I am ashamed of our sport today. Very much ashamed. This was a simple injury that would not have put this horse in any danger by any means and would not have made (Foster) gain any advantage in the ring."
Foster broke her back just before the 2008 Olympics and spent six months unable to ride. She said last week that she was very excited to be making her Olympic debut after a long road.
The Canadians filed a protest earlier on Sunday but the FEI ruled that there was no possibility of appeal in these cases.
Canada's Ian Millar, making a 10th Olympic appearance at 65, said: "Our team, all the riders, are devastated by this situation. We feel it's just not right and it's an incorrect application of the rules."
In Beijing, there was a rash of doping cases involving a chilli pepper derivative that, if used on a horse's legs, would increase susceptibility to pain.
The Canadian team will now have only three members in contention in the team final that wraps up on Monday, which means all scores count. Other four-member teams are permitted to drop their weakest score from the two-day total.
"I sure hope Canada can win a medal for her," Lamaze said.
Canada's Mac Cone was knocked out of the team final in the 2008 Games when his horse was injured, leaving the team in the same position, but they managed to take a silver medal.
"I am sick about it. Having said that, we did it before in Beijing and we got it done, but it's doing it the hard way for sure," said Millar.
It has been a tough Olympics for the Canadian equestrian team so far with the nation eliminated by falls or errors before the team finals of both eventing and dressage.