Chainrai, a former owner of the club, had been in pole position to buy the Fratton Park outfit through his Portpin company.
He had called upon administrators PKF to reduce the £1.8million in fees they wanted for overseeing the sale process, arguing that everyone else at the club had accepted substantial cuts.
"Portpin Ltd regrets to announce that it is withdrawing its bid for Portsmouth Football Club," read a statement released to Sky Sports News.
"Unfortunately, our efforts to save the club once more from extinction have hit a wall of rejection and lacking co-operation from the administrator and other interested parties.
"We are not the ones who have caused the club to collapse and we are not the ones to choose PKF as administrators.
"As history has recorded, we sold the club over a year ago after saving it from liquidation and unfortunately found ourselves again fighting to try and save the club from another liquidation.
"Through this administration process over the last six months we have always had the club's best interest in mind - unlike many parties who were involved in the process.
"We repeatedly encouraged the administrator to find a new, willing and able buyer to take over the club - unfortunately he was unsuccessful in this job and couldn't find a buyer despite his promises!!
"Later he approached us to be his safety net to save the club as he couldn't find a buyer. We agreed in the effort to avoid liquidation of the club. We welcome and will assist anyone, including the supporters trust to try and save the club in the coming days."
Chainrai was angered by the Football League's decision to deduct the club 10 points ahead of the forthcoming season.
He was also angered by comments from manager Michael Appleton, who claimed the club were certain to be relegated this season.
He had also labelled Chainrai as unprofessional after reducing his playing budget for the season, should the takeover go though, from £4million to £1.5m.
"We call on Mr Chainrai to do the decent thing and accept the PST offer to purchase his charge on the club, and therefore walk away from Pompey, regaining some of the money he has lost, and leaving the club in the hands of the people who will truly cherish it and ensure that it continues as both a business and a legacy for the future," read a statement from the supporters trust.