The board called time on the club's 100-plus years existence on Tuesday after entering into a Company Voluntary Agreement with creditors in January last year.
York chief executive
Ann Garvey
However, Greenfield admitted financial pressures at Huntington Stadium had proved too great.
He told BBC Radio York: "The last thing we wanted to do was close down rugby in York.
"It was a shocking decision we had to make. I feel so sorry for everybody, but we didn't have the capital to do it."
Coach Leo Epifania and his players were said to be "stunned" at the news.
"It's a sad day for rugby league and a very sad day for York," said York's chief executive Ann Garvey.
Hand-to-mouth existence
"The directors didn't want to let the club get into the state it's been in previous years so they took the decision to close it.
"I'm devastated and I feel so sorry for the players and for Leo Epifania, who gave up a business and a home in Australia to come over here."
The club, formed in 1901, almost went out of business last season and, despite landing a famous sponsorship deal with the New York City Corporation, have led a hand-to-mouth existence this season.
They were watched by a crowd of just 280 at their last home game against Chorley, which brought them their only win in 11 matches in the NFP.
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