The NSW Health Minister has brushed aside criticism of a bungle that led to 160 students at an elite Sydney school skipping the queue for COVID vaccines.

The year 12 students at St Joseph’s College received their first dose of the Pfizer vaccine in May, despite the general public still having only restricted eligibility for the shot.

Quizzed on Wednesday about whether the bungle was embarrassing for his department, state Health Minister Brad Hazzard urged people to move on.

“What I find more embarrassing is that you would make that sort of question and accusation against front-line health staff who work their butts off and will have tomorrow achieved 1 million vaccinations in arms,” he said.

“You know what? The school intended it well. There was a mistake and so what? It’s happened. Out of a million vaccinations. Move on.”

NSW Health has apologised for the “error”, which led to many of the 163 boys at the exclusive Catholic school getting a COVID shot before they were strictly eligible.

Amid tight supply, vaccines in Australia remain restricted to those over 40 or in other high-priority groups. Indigenous people and Torres Strait Islanders over 16 are among those considered high-priority.

In a statement on Tuesday, the school confirmed it had approached Sydney Local Health District about the vaccination because the 163 boys were boarders. Some of them come from rural communities, including remote Indigenous communities.

Sydney Local Health District chief executive Teresa Anderson said only Indigenous students were supposed to be vaccinated.

“Through an error, the wider group of boarders in year 12, a total of 163 students, were also vaccinated,” she said on Tuesday.

“Sydney Local Health District apologises for this error.”

School principal Ross Tarlinton said students were administered the vaccine at a centre determined by NSW Health.

“The approval and administration of the vaccine was endorsed and managed by NSW Health through the Sydney Local Health District,” he said.

“Acknowledging that the college does not determine vaccination priority, it welcomed the opportunity to offer the vaccine for students given the approvals provided.”

The vaccine bungle has sparked outrage, with NSW Teacher’s Federation senior vice-president Amber Flohm, blasting it.

“It’s obscene. Absolutely obscene,” she told the ABC.

“It highlights the inequality that exists across our society. That sort of behaviour is not going to get us through a pandemic.”

Ms Flohm said teachers’ requests to be considered high priority for vaccines had “fallen on deaf ears”, while privileged sections of the community were given doses.

“That is wrong on multiple levels,” she said.

“Teachers would be feeling that, as would parents.”