The Ibrox chief executive said on Wednesday he believes Rangers should attempt to leave Scottish football if league reconstruction plans are approved. The Scottish Premier League and the Scottish Football League this week agreed in principle to a restructuring plan that would see the organisations merge in a 12-12-18 structure.
Green is unhappy with the proposals which, if implemented for next season, would mean another campaign in Scottish football's bottom tier for Rangers, regardless of title success in the Irn-Bru Third Division this term.
Murray - who was part of the Blue Knights bid to buy the club in the summer - told Sky Sports News: "I can partly understand his frustration. Charles Green has only been in Scotland for less than a year and dealing with administration in Scotland is a frustrating process."
He added: "I've left the board, I'm no longer involved, it's a new era at Rangers and it's got off to a good start. If we're using that era to try to rebuild bridges within Scottish football, I think Charles Green and the Rangers board should actually rise above some of the things.
"Believe me, no-one is more frustrated with what happened last year than me. But I think it's now time for us to rise above that and actually provide leadership to the rest of Scottish football. I think Charles Green is well positioned to do that.
"With regards to leaving Scottish football, that's been discussed for many, many years. I'm sure there will be a restructuring of European football at some point, but when that will be I don't think anyone knows. I think Charles Green and the Rangers board should be more focused on improving Scottish football from within."
Murray lost his place on the Ibrox board following Craig Whyte's ill-fated takeover of the Glasgow giants, before joining forces with the Blue Knights when the club was forced into administration.
Asked if Rangers have an obligation to act in best interest of Scottish football as a whole, he said: "That's a difficult question. First of all they have to look after their own interests but clearly in any competitive sport you have to have people to play against. You have to have an interest in the bigger picture as well. Both things are important.
"I wouldn't say they've got an obligation but I think they are better suited to trying to improve the game from within Scotland than threatening to leave. I'm not quite sure what that really achieves. There is no point threatening to leave if there are no options. He should use his position from within to try to engineer change."