Purtell, 27, complained of feeling unwell after the game at Manchester's Etihad Stadium and received treatment from the club's medical staff on the team bus on the journey home. He was taken to Leeds General Infirmary where he underwent surgery and is expected to remain in hospital for the rest of the week.
"Adrian had an immediate primary angioplasty to remove the blockage in his artery but both the club and the player wish to point out that at no time did he suffer a cardiac arrest," said Bradford football manager Stuart Duffy.
"His heart did not stop beating and he was conscious throughout the journey to hospital.
"Adrian is feeling much better today but will remain in hospital for the next few days for further tests."
Bradford say they were unable to initially comment on Purtell's condition until receiving his permission due to patient confidentiality, although the player's mother Fran Purtell broke the news to an Australian newspaper just before catching a flight to England.
Duffy added: "The Bulls would like to thank the club's medical team, Dr Donald Young, physiotherapist Jamie Moseley and head of conditioning Geoff Evans for their treatment of Adrian and in particular the staff at both the Huddersfield Royal Infirmary and the Leeds General Infirmary for their expert care of Adrian.
"The club would also like to thank the RFL for their support in this matter."
Purtell, who is in his first season in Super League, issued a statement through the club thanking everyone for their best wishes.
"I have read all the messages and would like to thank everyone for their concern," he said. "The response from the rugby league community has been overwhelming and I appreciate everyone's kind thoughts."