The failure cost the school system $250 million in school education aid, the New York Post reported.
Cuomo said failure to resolve contract issues before the midnight Thursday deadline was "a tragedy," noting that New York was among "a very small handful" of cities that could not reach agreement.
The governor said he had refused requests from both sides to extend the deadline.
"You extend a deadline and the next time you say it's a deadline it's really not," he said.
"I don't know who's right, who's wrong," Cuomo said. "But I know they both failed because we needed an agreement and now the education system in the city is going to suffer."
New York Mayor Michael Bloomberg called the lack of a contract "deeply regrettable."
"We were actually very close," he said. "But unfortunately, every time we approached a deal in recent days, the [United Federation of Teachers] moved the finish line back."
UFT President Michael Mulgrew disagreed with the mayor's version of negotiations and repeatedly called him a liar. He said the union had an agreement but the mayor interfered with it.