Mr Gvozdanovic said he was told an ACT ranger from Canberra's Domestic Animal Services (DAS) had ordered that the dog be put down only 24 hours after she had gone missing.
He said this was despite DAS policy saying that impounded dogs are required to be held for seven days, with dogs either rehomed, sold or euthanased after this period.
But the ACT Government's city services directorate said Izzy was in "poor health" and her coat was "highly matted" when she was dropped into DAS about 5pm on June 10 by a member of the community after Izzy was found "roaming unaccompanied in Kambah"
"The dog appeared to be in poor health, its coat was highly matted and it was found to be deaf and blind, with both eyes ruptured and needing significant treatment," the spokesman said.
"Both DAS and the treating veterinary practice attempted to contact the owner via the details found on the microchip, however the recorded details were not current and after a number of attempts contact was unsuccessful.
"After further liaison between DAS and the treating veterinary surgeon the dog was euthanised.
"DAS are currently investigating the matter further including talking with the owner, and as such further comment cannot be made at this time."
Mr Gvozdanovic said he was under no illusions that Izzy was in the best of health, but argued she was microchipped, wearing a coat and was clearly identifiable as a pet.
"She was just an old dog, she's not a wild dog," he told ABC. "I'm not deluded in thinking she wasn't approaching that moment when I would have to make those decisions, but … she was still happy in my opinion.
The distraught owners wants answers to why Izzy was put down so quickly without him being consulted.
"Something has gone majorly wrong here," he said. "I hope this is a one off … I hope animals aren't being killed at the convenience of the Government.
"I believed that by registering her details and having a seven-day time frame to react was sufficient to deal with this situation but that was taken out of my hands."
The ACT opposition urban services spokeswoman Nicole Lawder wants answers, asking city services minister Meegan Fitzharris "to advise as a matter of urgency how this sad event has taken place within hours of a much-loved elderly family pet going missing".
The issue was raised in Assembly Estimates this morning, where Mr Gvozdanovic was told by ACT director of city presentation Stephen Alegria that Izzy's death was being looked into.
"Sorry about what's happened," Mr Alegria said. "We're investigating this matter very seriously, so I think it's probably not very helpful to try to predict the outcome."