The series, which stars Dustin Hoffman, explores the lives of several characters caught up in the world of horse racing.
The official website for the American Human Association confirmed that two of the animals were put down after becoming injured - one during the filming of the pilot and one during the filming of the seventh episode.
"The two racehorses stumbled and fell during short racing sequences," the AHA explained in a statement. "The horses were checked immediately afterwards by the on-site veterinarians and in each case a severe fracture deemed the condition inoperable. The decision was that the most humane course of action was euthanasia.
"American Humane Association is deeply saddened by the deaths of these two wonderful animals. Because of these accidents, the two episodes in question do not carry the full certification, 'No Animals Were Harmed'®."
However, in a post on its own website, PETA criticised the deaths, insisting that it had "repeatedly reached out" to series creator David Milch and the show's production team, only to be "rebuffed".
"Two horses died for a couple of hours of television!" wrote the group. "Perhaps if producers had considered the proved safety protocols that we would have suggested, these horses would still be alive.
"The show's theme is showcasing the dark side of racing, and while it does acknowledge how many thoroughbreds suffer catastrophic breakdowns and how horses are routinely doped, two dead horses in a handful of episodes exemplify the dark side of using animals in television, movies, and ads."
The post continued: "We... are now in discussions with HBO about how to prevent even more deaths on the show."
Luck airs on Sundays at 9pm on HBO in the US. The show will air on Sky Atlantic in the UK.
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