New York City Council Speaker Adrienne Adams tried to defend her approval of the city’s controversial education budget by claiming Thursday that she “held up” negotiations on the deal to cut funding — even though the plan was passed in record time.

Adams made the claim after signing a letter to Mayor Eric Adams in which she and a large group of other politicians who voted for the plan — and who now oppose what they voted for — tried to get the city’s executive to help reverse their error by claiming they failed to understand what they were doing.

“What I can let you know is that we have an entire New York City to take a look at in negotiations,” the Queens Democrat told The Post Thursday during a press conference at City Hall when asked why she’s having a change of heart.

“So, in those negotiations, we take a look at a really, really gigantic picture. We don’t carve out certain agencies over other agencies – we take a look at the total picture.”

The Speaker then claimed she “held up negotiations” over the funding cut.

In a letter to Mayor Adams sent Wednesday, the speaker took issue with cuts in the city’s record-busting $101 billion budget — even though the education plan was approved three weeks before its due date on July 1.

“DOE’s numbers are not adding up, and it seems to be using the city budget as a smokescreen to evade responsibility for its policies that undermine support for schools,” the pols whined in the missive, signed by 41 Democratic members of the 51-member City Council.

The deal that Speaker Adams wants undone cuts hundreds of millions in city dollars from a funding pot that permits city schools the authority to hire their own teachers and principals.

The cuts range from an estimated $215 million, according to the City Department of Education –  but City Comptroller Brad Lander said in budget testimony during a recent council hearing the slash could be as high as $469 million.

But Mayor Eric Adams slammed the door on their request.

“We both approved. They read the bill, they saw the budget, they voted on it. Partnership that’s what we did,” he said Thursday in Astoria, Queens during an unrelated event.

“They got over 90% of the things they asked for, and so we are always open to figure out how do we sit down and figure out how to run the city better together. But you don’t vote on a budget and then re-negotiate it. That is just not how the system operates.”

He said the cuts make sense because kids have been leaving the public school system, causing enrollment to drop.

“We have adjusted the class sizes. That’s getting lost in this narrative. If you’re giving people funding for 1,000 students and those students dropped out and there’s 600 – That’s not dysfunctional to keep giving them the dollar amount?”

He also indicated the city’s overall budget could face even worse cuts in future years, anticipating the drying up of federal coronavirus dollars directed to the city.

“We’re about to fall off a financial cliff once the stimulus dollars run out,” he said.