The news continued the club's dismal week after Tuesday's confirmation that their 12-point Premiership deduction would remain following a failed appeal.
A day later, Portadown conceded two late goals to lose 4-3 against Crusaders in the League Cup.
"I believe the time is right to step away - I've done all I can to move the club forward," said McGibbon.
After serving an interim boss following long-serving Ronnie McFall's resignation in early March, former Manchester United defender McGibbon was appointed manager in late April.
However, six weeks later Portadown were handed a 12-point deduction for this season's Premiership after an Irish FA disciplinary committee ruled that they had paid player Peter McMahon even though he had been registered on amateur forms.
Portadown were already facing a transfer embargo in addition to being fined £5,000 because of a further registration breach involving Gary Twigg.
The Shamrock Park club were handed a total ban from all football related activity in late July for a failure to pay the £5,000 fine and their first scheduled league game of the season against Coleraine on 6 August was postponed.
Portadown appealed against both penalties but their pleas were rejected by an Irish FA appeal panel last Tuesday.
"As a former player both at youth team and first team level, I am devastated to see the current state of the club," added McGibbon.
"Recent events have had a demoralising effect on players, management and supporters alike.
"Despite player restrictions and ongoing administrative issues, I have been working hard with Vinny, the players and the rest of the management staff to improve fortunes on the pitch.
"However, I have found that my roles and responsibilities have been taken up more as a general manager than from a first team management perspective.
"Vinny and the rest of the backroom team have been terrific in helping with training whilst I have prioritised and dealt with other issues."

His plan to boost infrastructure investment was welcomed by the British Chambers of Commerce and the Royal Institution of Chartered Surveyors.
Meanwhile, the Institute of Directors said his intention to renationalise the railways and to raise business taxes would undermine the UK economy.
It said business would "make its case".
The most positive response came from RICS.
Jeremy Blackburn, the organisation's head of policy said: "He has raised some challenging but principled issues around the expansion of Right to Buy to private landlords; as well as providing a voice for the widely-felt dissatisfaction of privatisation in our rail sector. There is undoubtedly opportunity in his agenda around infrastructure and public spending to get Britain building, and we look forward to sitting round the table and discussing this further. "
John Longworth, director general of the BCC, also highlighted Mr Corbyn's infrastructure plans: "Firms will be encouraged by recent statements favouring much-needed investment in the UK's inadequate infrastructure and skills.
"We will be looking for the opposition to take a pragmatic and practical approach to business recognising that wealth creation is the necessary prerequisite for the delivery of any political objectives."
But there was a warning from Simon Walker, director general at the IoD: "From renationalising the railways, to raising taxes on businesses and increasing government spending, Corbyn has proposed some policies in the leadership campaign that we believe would undermine our open and competitive economy."
Mr Walker added that business leaders were never in "perfect agreement" with politicians of whichever party, but that the IoD would give its views "sincerely" in discussions on matters such as state investment in infrastructure and excessive pay at big companies.
Crisis club Portadown are looking for a new manager after Pat McGibbon resigned on Friday evening.
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Jeremy Corbyn's election as Labour leader has received a mixed reaction from business, including a cautious welcome for his plan on infrastructure.