The past 12 months has seen a spectacular fall from grace for the Scottish giants, who entered administration on February 14th last year.
The months that followed saw the oldco club liquidated while newco Rangers, under the new ownership of a consortium fronted by Charles Green, were consigned to start life in the third division of Scottish Football.
Murray, who was appointed chairman of the club in June, is concentrating on the rebuilding process after a nightmare year for the Glasgow side.
The Gers' recent Scottish Cup defeat to Dundee United has seen pressure on manager McCoist increase from some sections of Rangers' fans but Murray is adamant he is the right man to take the club forward.
Asked if he was the best man for the job, Murray told Sky Sports News: "Yes. Because he's got more motivation than anyone you could bring in from outside. Motivation is the one thing.
"The players have got massive respect for him."
Questions have surfaced over where Rangers could be playing next season, with chief executive Green openly voicing his opposition to proposed plans for a reconstruction of Scottish Football which would see Gers remain in the bottom tier even if they achieve promotion this term, with the club chief even suggesting they could leave Scotland.
While Murray expects Rangers to stay north of the border for the next couple of seasons, he admits the prospect of a European super league is a real possibility.
"I think it's more likely we'll stay in Scotland for the next couple of years," he said. "I think, ultimately, the big brands will get together but it will take time."
Reports that Ibrox could be renamed as Gers continue the rebuilding process have been met with anger by fans.
Murray admits a name-change could occur, but that Ibrox will be kept in some capacity, adding: "Let's say it's possible but, like all fans, we would like the Ibrox name in it, whatever. We'll always call it Ibrox, that's what it is. But it must have Ibrox in it."
Green, speaking on Rangers' official website, says the club are focused on looking ahead after a difficult year.
He said: "I am acutely aware that 12 months ago, this great football club was plunged into a financial catastrophe - the impact of which is still being felt throughout Scottish football.
"However, today everyone involved at Rangers - the supporters, staff, players and our many business partners - can take great pride in the fact that not only did the club survive such a difficult time, it can look to the future with confidence and a firm belief that we can , again, achieve great things.
"All along, we have known that the rebuilding of the club on the pitch will take time and we are prepared for that. Given the events of the last year, Ally McCoist deserves everyone's full support as he and his team continue to make the Rangers team strong again."
To read more about how Rangers are getting on one year on from administration visit the club's official website here