The HBO racing series, which starred Dustin Hoffman and Nick Nolte, was axed on Wednesday (March 14) following the latest tragedy on set.
"Safety is always of paramount concern," a statement from HBO read. "While we maintained the highest safety standards possible, accidents unfortunately happen and it is impossible to guarantee they won't in the future."
California Horse Racing Board equine medical director Dr Rick Arthur, who worked with the production when it filmed at the Santa Anita race track, has now backed up the network by saying that there was nothing "outrageous" about the deaths.
"Accidents do happen," he told TV Guide. "It's not as outrageous as it's been played to be. Any of these accidents are not unique circumstances."
Meanwhile, an HBO spokesperson has responded to accusations from PETA that "old, unfit and drugged horses" were used on Luck.
"The drugs that have been referenced by PETA were administered post-injury to calm the horse and to allow the attending veterinarian to properly examine the injury," they said.
PETA had been protesting against Luck prior to the death of the third horse and said that they were "glad" of its axing.
Luck airs on Sundays at 9pm on HBO in the US. The show airs Saturdays at 10pm on Sky Atlantic in the UK.