McAllister informed his players of his decision following a challenge game on Saturday, and confirmed his departure on Sunday morning.
Several players have followed the former Coleraine skipper, who was in his second spell as manager of the west Belfast club.
Following a meeting with several senior members of the club last week, McAllister was informed of its dire financial position, and that there was no money for player wages or expenses.
What direction the club will take is anyone's guess - though it is rumoured it may return to its once-held amateur status, or seek to consolidate in the NIFL Championship for the foreseeable future.
Currently, not a single Donegal Celtic player has been registered with the Northern Ireland Football League - just five days before the new league season kicks-off.
It is believed also that a number of voluntary staff at the club, including chairman Gerard Rooney, have quit.
Pat McAllister, who ended his 20-year playing career at Donegal Celtic, said: "I have reluctantly taken the decision to stand down from my position of first-team manager at Donegal Celtic Football Club.
"It was with a heavy heart that I reached this decision but felt that the conditions explained to me by the club ahead of the new season did not match my ambition as a manager, not my ambition for the team and its players.
"It is my firm belief that Donegal Celtic Football Club should be competing in the Irish Premier League and it was my sole aim to achieve that status once again, for the club, and for the community."
The statement continued: "I truly believed that with the squad I had convinced to remain at the club following relegation last season, we would return to the Premier League at the first attempt.
"However, circumstances have changed and unfortunately, for sake of my career, and those of the players, I could not operate under such conditions and restrictions."
I demanded the highest standard of dedication and professionalism of myself as a player, and as a manager. I could not allow standards to slip, nor could I expect to demand the same of the players when circumstances out of my control could ultimately effect the level of dedication and professionalism in the squad. I wish the players every success in what will be a challenging season in a challenging time for the club.
Pat McAllister, ex- Donegal Celtic manager
Celtic skipper Paul Bradley took to Twitter to confirm his departure, using the hastags #onceagreatclub and #shamblesnow.
It is understood midfielder Ciaran Gargan, defenders Mark Burns and Eamon Hughes and promising midfielder Pearse Devine have all quit, while more departures are imminent.
Last season former Donegal Celtic manager Paddy Kelly quit in a blaze of controversy and following a five-year suspension handed down to then chairman Raymond Bonnar, and former secretary Hugh Greene.
Kelly's departure saw a number of other key personnel leave Celtic Park too.
Then McAllister returned for his second spell in charge, after former Ards player Declan McGreevy was forced to stand down just days after he succeeded Stephen Small due to not have the required coaching qualifications to meet for Irish Premiership criteria.