Farrell quit on Saturday night after agreeing to take over the manager's role at Dumbarton.
That was followed on Sunday by the shock resignation of Dougan from his position as chairman and from the club committee.
Vice-chairman Shaun Niven said Mr Dougan's resignation had been prompted by the publication of resignation statement from three former committee members who claimed they had “profound concerns” about the way the club was being run.
It was claimed that the atmosphere at recent committee meetings had been “toxic” and that the three had been excluded from key decisions.
The three also alleged that they had not been provided access to essential financial documents to enable them to make informed decisions on the club’s future.
Mr Niven said the chairman’s resignation had been accepted reluctantly.
He said: “He [Mr Dougan] feels that the accusations levelled against him are of such a nature that he could not continue in the role.
"He has expressed his disgust at having his honesty and integrity questioned in such a venomous and inappropriate public way and that the attempt to besmirch his reputation has gone way beyond that which is acceptable.
"Iain has expressed that his first loyalty must be to himself and his family.
"He also expressed his disgust that the club has once again been subjected to the mistrust, ridicule, rumour and innuendo that has been such a burden to us in the past and that the club has worked tirelessly to try to repair over the past 15 years or so.
"The destabilising of the club at boardroom level coupled with the current uncertainty on the management front can in his view, only end badly and as a result with deep regret he wishes to remove himself from the situation.
"As vice chairman, I have nothing but the utmost sympathy and respect for Iain, who has done a fantastic job as Chairman over the years, none more so that his dignified and passionate championing of the cause of Stranraer FC during the turmoil of the recent pandemic.
"This is a sad day for the club and for me personally and frankly, Iain deserves better. I share his disgust at the comments that have been made online which, in my opinion, appear to have the express intention of deliberately damaging the club, the committee, or both and I am advised to make that my only comment on that matter at this time."
Mr Niven said that it had been incumbent on him to seek the approval of remaining seven committee colleagues to act as chairman for the interim period.
He added: "They have given me their backing to do so and I express my sincere gratitude to them all for that."
The news broke as Stranraer fans were already coming to the terms with the departure of manager Farrell who is returning to Dumbarton where he was number two to Stevie Aitken between May 2015 and January 2017.
Assistant Frank McKeown is moving with him.
A club statement said: "Faz will be sorely missed around the club, and our thanks go out to him for his efforts and commitment over the past four and a half years.”