"But your referees will pay now for their erorrs, be sure in that and you will see all soon.
"We will find them and we know now a lot about them. They are on target now."
An online petition, which has already attracted more than 23,000 signatures to have Mr O'Leary sacked from the tournament, emerged after an image appeared to show him "celebrating" with Nigeria goalkeeper Vincent Enyeama after the final whistle.
Comments posted on the petition page at change.org include people threatening to "burn him and his house" and "Die Peter O'Leary! Just die idiot".
But friends back home, as well as national governing body New Zealand Football have backed the 42-year-old's performance in the match.
New Zealand Football referee development officer Ken Wallace said Mr O'Leary, along with his referee assistants, fellow Kiwis Jan-Hendrik Hintz and Mark Rule - who wrongly ruled out a Bosnia goal by judging striker Edin Dzeko offside - will now go through FIFA's review process.
Mr Wallace spoke with Mr O'Leary after the match.
"Peter's good. Obviously, he's frustrated by the fall-out, but I thought he had a very good game and looked like a top referee. He was happy with his performance, and so he should be, too."
New Zealand Football said it is aware of the death threats and are working alongside police.
However, it had no concerns for the personal safety of Mr O'Leary, a science teacher at Tikipunga High School in Northland.
"The security around referees in Rio de Janeiro is fantastic. I don't imagine there will be any issue at all," Mr Wallace said.
"We're hoping things will settle down and people just take a deep breath."
Fellow football ref and long-time friend Brett Chibnall said the criticism amounted to a "gross overreaction".
"It's all gone a bit silly, hasn't it," he said.
"Humans play sport, and humans make mistakes. So if there's a mistake, you have to live with it."
Perhaps the only person in New Zealand who knows just what Mr O'Leary is currently experiencing is Mike Hester, the only other Kiwi to referee a World Cup match - Korea Republic vs Greece in the 2010 World Cup in South Africa.
Hester, now a Lieutenant Commander with the Royal New Zealand Navy, believes the Kiwi officials will be "disappointed" by the offside decision.
But he has no concerns over their safety, with referees surrounded by security going to and from stadiums, "irrespective of how heated a match has been".
He says it will soon blow over, and hopes Mr O'Leary - who he knows well - gets another game during this tournament.
"The unfortunate thing about officiating is that there's always going to be someone that's unhappy and it's the officials who wear the brunt of it.
"That's all part of it, unfortunately. But at the end of the day, it's just a reaction. That's all it is."
