The businessman, who heads Portpin Ltd, was expected to complete a takeover of the club after administrator Trevor Birch offloaded a host of first-team players in order to drop the wage bill.
"Portpin Ltd regrets to announce that it is withdrawing its bid for Portsmouth Football Club," Chainrai said in a statement 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. 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!!"
The former Championship club fell into administration for the second time in two years in February.