In accordance with Football League rules, County are given a 10-point penalty and fall from 13th to 18th in league football's third tier.
Chief executive Sean Connelly told BBC Radio Manchester: "I am absolutely gutted and frustrated.
"We were so close to having everything put into place to guarantee a long-term future for the club but we don't know what's going to happen now."
County now lie just three points above the relegation zone and need a draw in Saturday's final game of the season at Brighton to be mathematically certain of avoiding relegation to League Two.
606: DEBATE
Provided we can stay in business, we can come out of this smiling
Sheff Hatter
The club have been fighting to stave off administration but their level of debt, with one creditor owed £300,000, has made it unavoidable.
"We went so far, this morning, as to offer our creditors a large part of the payment directly into their account in earnest of our intent going forward but obviously that didn't get taken up," said Connelly.
"To have the rug pulled from under us like this is simply soul destroying. I know the staff here are just destroyed by it."
John Titley and Paul Reeves of Manchester-based accountancy firm Leonard Curtis confirmed that they had been appointed as joint administrators.
"We are keen to work with the board to explore all possible solutions to ensure the club's future prospects are protected," said Titley.
"We are extremely hopeful we will find a buyer for the club and are already aware of expressions of interest."