The former oldco Rangers director won an interim interdict at the Court of Session on Monday which blocks Ibrox chief executive Mather from staging the club's annual general meeting on October 24.
Murray, however, does want seat on the board but now hopes a shareholder vote will secure it.
He claims he has already turned down an offer from Mather that would have seen him join a new-look board alongside Dave King - but only if he had dropped his legal action and walked away from a partnership with billionaire businessman and Rangers shareholder McColl.
Clyde Blowers chairman McColl was behind a previous bid to oust Mather from the board.
Asked if he was confident he can now win over shareholders at a rescheduled AGM, Murray said: "That is for the shareholders to decide. I will present my credentials in the days to come. I have always told the shareholders, 'If you don't want me on the board, don't vote for me'.
"I think I can add value to the board. As you probably know, I was offered a seat on the board last week. But the condition of that was that I gave up today's hearing and that I effectively ditched my colleagues like Jim McColl and the shareholders who supported us and I just won't do that.
"People think I want a seat on the board at all costs but I have got certain principles and I will stand by those principles.
"All I ever wanted for the club - and I have never taken a penny out of it - is what is in the best interests of the club."
Murray, who led the unsuccessful Blue Knights bid to buy Rangers before they went into liquidaton, was forced to act after Mather and his fellow directors refused to add a motion calling for four new directors to be appointed at the AGM, including himself.
Murray hoped to be joined on the board by former chairman Malcolm Murray as well as backers Scott Murdoch and Alex Wilson but their resolution was denied when the board claimed it was not "validly executed".
However, Lord Tyre ruled on Monday that there was "no valid legal reason" for the Rangers directors not to present Murray's motion to the rest of the club's shareholders.
Rangers must now stage an AGM by December 30 and must give shareholders at least 21 days' notice.
Paul Murray - who was also awarded costs for Monday's hearing - did welcome news that former director King was close to agreeing his return to the board.
The South Africa-based businessman lost £20million when the club went into administration last year but could return as chairman.
"I have always said that Dave King is a very good guy on a whole number of levels," said Murray outside the court. "I have always been supportive of him and I'm delighted he's involved in the club again.
"He has his own plans and he has recommended to the board that I might be a useful addition.
"I am prepared to join the board but I am not prepared to give up my principles."
During the court hearing, Murray's lawyers accused Mather and the other Ibrox directors of engaging in "guerrilla warfare" in their battle against the former Deutsche Bank executive.
Richard Keen QC also claimed that the Rangers board may have broken the law by failing to tell the rest of the club's shareholders about Murray's bid in sufficient time before the planned AGM on October 24.
He said: "An offence has been committed by every member of this board.
"The board have placed themselves in a very difficult situation by failing to discharge their statutory obligations. They have committed an offence.
"If I am right, the consequences of that must be visited upon them."
The court defeat was the second embarrassment for the Rangers board on Monday after they were forced to publish amendments to weekend statements which suggested King had been lined up as chairman to lead a new fundraising bid.
Rangers released a follow-up statement to the London Stock Exchange claiming that King's position would be on the football club board, which is the company formerly known as Sevco Scotland, and not the plc board.
The club, who last month announced an operating loss of £14.4million, said: "At the insistence of our nominated adviser, the board needs to make it clear, for regulatory reasons, that the board of directors referred to above is The Rangers Football Club Limited, the wholly owned subsidiary of The Rangers International Football Club PLC.
"Although we welcome the support of Dave King, no decision has been made to appoint him as a director. There are regulatory matters which would need to be resolved prior to any such appointment.
"The directors also expect that in the medium-term future, possibly coinciding with the return to top league football in Scotland, it may be in the best interests of the company to raise further capital.
"However, there is no requirement for short-term funding, and as such neither the company nor RIFC are actively seeking finance. Nonetheless, we are committed to exploring a future involvement by Mr King in the club."