The players became free agents and Lincoln City manager Chris Sutton was desperate to have wideman McClean in his squad for the crucial League Two derby game against Grimsby Town on Saturday, which ended in a goalless draw.
However, the FAI have blocked the Northern Ireland Under-21 player's move until the transfer window opens in January.
Carlile said that "common sense must prevail" under the extraordinary circumstances.
"Some of the Derry City players haven't been paid in 11 weeks and they have been told that they are free agents," he said.
"But I have been told that they can't sign for another club until the transfer window opens.
"I understand that there are rules but surely this is a special case.
"Lincoln have told me that the FA will be in touch with FIFA to try to sort the situation out.
"It is a ludicrous situation. The players have been punished enough.
"That is another six weeks that the players will be denied the opportunity to earn a living.
"We have the FAI looking for a moral judgement from FIFA and the French FA following Thierry Henry's hand ball in midweek but they are prepared to leave players without any money in the in the run-up to Christmas - and you are not talking about players who were being paid £10,000 per week at Derry City.
"Where is the morality in that?
"The players have mortgages and bills to pay and some of them are spiralling into debt.
"Common sense must prevail and it is a matter of urgency."
Sutton told Press Association Sport: "I am not 100% sure what has happened over in Ireland with Derry City but we are keen to get James signed.
"There is only one loser here and that is the player."
Former Derry City player Niall McGinn, who signed for Celtic in January, revealed his worries for his ex-team mates.
"It's disheartening for the guys," he told the Sunday Mail.
"Two players - Mark Farren and Barry Molloy - are getting married.
"People also have mortgages to pay and I realise how fortunate I am."
Despite repeated calls to the FAI, no-one was available for comment.