And despite pressure on Shaw to try pull the funding, Finance Minister Grant Robertson has ruled out doing a U-turn.
"The Government has made an agreement here," Roberson said.
"I can understand that there are people who perhaps don't like it or would rather the decision was changed. The Government's got to act in good faith here with an applicant, so I've got no intention to [reverse it]."
Shaw advocated for an expansion of the Green School in Taranaki, which charges up to $43,000 a year in fees for international students, to get money from the $3 billion infrastructure pot in the Covid-19 Response and Recovery Fund.
Shaw said he advocated for the project because it was sustainable infrastructure which promised to help diversify the region's economy from depending on oil and gas.
It was a green infrastructure project which happened to be a school, he said.
But when it was announced by Shaw in his role as Associate Finance Minister on Wednesday, it was met with horror from public schools and fury from some Greens members.
One of the party's core principles is ending public money going to private schools.
The acting principal of Marfell Community School, a low decile school in New Plymouth, Kealy Warren, in an open letter said the funding was "totally unacceptable, elitist, and completely inequitable".
"I am totally insulted by this action, I am livid, hurt and want to scream until we are heard."
"I felt physically sick, I wanted to vomit. I could not believe we were being so disrespected in favour of an elitist private school."
She says it sent a message of worthlessness to her students.
"I'm heartbroken for our beautiful children that have been told yet again you're the bottom of the heap stay there - what are you going to amount to?
"You're the bottom of the heap, just stay there, you're not going to add to the economy when you grow up so sit there in your leaky classroom," she said.
Four former Green MPs took to Twitter to express their disappointment. Sue Bradford described the move as "incredible" and Mojo Mathers said she was "furious".
A meeting of the party's membership has been called on Friday night by the Greens' Policy and Party co-conveners to ask for "information and clarification" from Shaw and co-leader Marama Davidson.
Shaw said he had heard calls for him to resign as co-leader but did not think this was a resignation issue.
But if given the choice, Shaw said he would think twice before pushing for the project again.
"I certainly think in hindsight, given the sense of distress that teachers and principals feel about their own schools having not yet gotten what they need in order to repair their own estates, I would think twice about it."
And with recent polls putting the Greens right on the knife-edge 5 per cent threshold to get back into Parliament, Shaw said he hoped voters would remember the party's record on climate change, inequality and conservation.
"I don't think one mistake is enough for people to switch."
Shaw couldn't comment on whether he was attempting to get the funding pulled - but said requests for that to happen had been made to him by unions, teachers, principals.
Robertson has ruled that out however, saying the Government was obliged to honour the agreement.
"My view is that the Government has a good faith obligation to the people that have applied and been told they have received money."
About 1900 applications were made to the Infrastructure Reference Group which Crown Infrastructure Partners shortlisted to 800 for ministers to assess before 150 were agreed on.
Robertson said the Green Party had advocated for the Green School but supported the position it was assessed purely as an infrastructure project.
He said the funding was a separate part of Government from the education budget - which last year committed almost $400 million in funding to every state school for property improvements.
- additional reporting RNZ
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Comments
This is tragic for the greens.
This just proves to all that the greens can be as two faced as anyone. Does anyone still believe anything they say or do they need more evidence?
You could say the Labour Party arm of the COL is as equally responsible too as they Labour as the purse holders must of approved the funds either directly or indirectly to enable the Green leader to donate such a disgusting bloated sum of money to this private green orientated school of education and ideology. So much for so little return...
The Government has a good faith obligation to the people to spend taxpayers money for the good of the majority or for the disadvantaged to ensure society's hand reaches meaningfully to include them. This is a tragic spend of a huge amount of taxpayers money to the privileged with money.
A "mistake" like this is more than enough reason to switch. It's a complete sell out and if you're not punished you will not learn.
This isn't incompetence, this is corrupt.
No surprise really, never been able to trust the Greens and they should never be let near the centre of power. Hopefully they will be out with Winston soon.
Moral of the story... never vote for the Greens.
I seem to remember misappropriation of benefits by another Greens leader just before the last election.
Poor decision making seems to be a regular thing for these people... Especially when it comes to taxpayer dollars.