The former England captain was axed on Tuesday after a run of form which had seen the Seasiders lose nine of their last 10 games, a sequence which had led Blackpool Supporters Association to call Ince's position 'untenable' in an open letter to Oyston on Monday night.
Oyston then dismissed Ince, along with his two assistants Alex Rae and Steve Thompson, after claiming the managerial team had failed to produce a list of transfer targets - something they had been asked to do following a crisis meeting on Sunday evening.
In an interview on Sky Sports News on Wednesday, Oyston confirmed rumours that the three men had been informed of their sackings via text message as well as by letter because they had been unreachable with Ince away on a coaching course.
The Blackpool chairman made it clear he did not wish to air the dispute in public but, via a statement through the League Managers Association, Ince has hit back at Oyston.
"Further to being sacked as manager of Blackpool this week, I feel it is necessary to release a formal statement to provide clarification on certain key matters," Ince, who lasted less than a year at the helm, said.
"First, it was deeply disappointing to have been notified that my contract was to be terminated via text message after a lengthy meeting with the club chairman on Sunday where no indication was given that any of the coaching staff, myself included, were going to lose their jobs. Neither I nor my coaching staff received a telephone call from the chairman at any stage after this meeting.
"It is true that I was at St George's Park this week as I am completing the final phase of the UEFA Pro Licence, which I have been working towards over the past two years. Along with others in my position, I have attended several such training days throughout this period. As a result, I had arranged for both Alex Rae and Steve Thompson to oversee matters at Blackpool's training ground.
"It also disappoints me that I have been accused of failing to produce a transfer target list. Whilst recent results have been of concern, especially after we enjoyed the best start to a season in Blackpool's history, we had identified key targets in the January transfer window to improve the squad as a result of injuries to key players and the loss of four loan players who returned to their parent clubs. The need for new faces at the club could not have been more evident than at the recent home match against Middlesbrough where we had two young players on the bench who had already played in another match that morning.
"Overall, my time at Blackpool has been a great learning experience. Having joined in difficult circumstances when we were fighting relegation, it was great to have retained the club's Championship status and then make such a positive start to the season after losing several senior players over the summer. After starting the new campaign with just 18 players available, and then losing some key members of the squad over the Christmas period to injury, it was clear we needed to strengthen to ultimately improve results and that is what we were actively trying to achieve.
"I enjoyed working with the chairman during my time in charge. We had a very good professional relationship so it is with sadness to have been relieved of my managerial duties, and the manner in which I was informed of my dismissal was particularly disappointing. I would like to thank the staff who have assisted me in every possible way, the players for their great efforts and the fans for the support they've given me during my time in charge. I wish everyone connected with the club the very best for the future."
Oyston revealed he had taken the supporters' feelings towards Ince into account when making his decision.
"It was absolutely unanimous - everybody wanted Paul Ince to leave the club," Glenn Bowley, chairman of the Blackpool Supporters Association, told Press Association Sport.
"You should never get personal but everybody there felt we would have a better chance of improving and getting out of this poor run that we're on if Paul Ince wasn't the manager."
The Sky Bet Championship club, who still have Ince's son Thomas among their ranks, have placed ex-Scotland captain and current Seasiders player Barry Ferguson in temporary charge this weekend for their home clash with Doncaster at Bloomfield Road.