And he branded the players who had left the club "disrespectful to everyone at Rangers".
Murray said: "The vicious and gratuitous blood lust of recent times must end, not only for Rangers' sake but for Scottish football too."
He added: "Certain individuals must ask some searching questions of themselves as to what their true motives have been over the last few months and whether they really have the best interests at heart of the club they claim to love and support."
He called on fans to renew their season tickets and for individuals, including ex-player John Brown, to join as investors.
Murray confirmed that staff and players were still being paid as scheduled and would continue to be so.
A total of 13 players reported for pre-season training yesterday – the day their monthly wages were due – but at least 10 have refused to join the new company.
Murray said: "It was extremely disappointing that a number of players have chosen to leave.
"It was disrespectful to everyone at Rangers and to the fans not to be honest about the financial gain they will receive in return for walking away from the club that has supported them over many years.
"The clauses they negotiated in return for the temporary wage cut during administration, would have enabled them to easily move on from Rangers with our blessing. Their actions have deprived the club of significant transfer fee income."
He made the statement after 1500 Rangers fans protested against Charles Green and his team outside Ibrox stadium on Wednesday night.
The were addressed by club legend John 'Bomber' Brown, who is attempting to lead a fans' buyout.
Green has already rejected two offers since buying the assets and business of Rangers for £5.5m two weeks ago and has faced criticism over a lack of clarity surrounding his investors and scepticism over funding available.
Murray also said that any boycott of season ticket sales would only do further damage.
He added: "Such action would only serve to help destroy the very institution that is so dear to us.
"The club has new banking facilities in place and, as stated a number of times previously, all season ticket money will only be used for the benefit of the club."
Murray stressed working capital was in place and that Craig Whyte, who took Rangers into administration, was not involved in Sevco.
He also insisted that the company, which they hope to rename The Rangers Football Club, owned all the old club's assets.
He said: "Craig Whyte has NO involvement with the club, in Sevco, The Rangers Football Club or any other of the consortium members.
"Indeed, measures have been implemented to ensure that Mr Whyte could not return to the club in any way, which is in compliance with the SFA's ruling on his participation in Scottish football.
fiona.mckay@heraldandtimes.co.uk
