The scathing attack on Green came just a day after the businessman, who stepped down from his former job with the club in April, returned to Rangers as a paid consultant.
As turmoil gripped the club last night, chief executive Craig Mather also came out fighting, describing the attempt by a rival group to remove him from the board - along with two other directors - as ill-considered and ill-timed.
McCoist spoke out after Green reportedly warned McCoist that Rangers must win a cup this year and that securing the League One title was not enough.
Rangers' week of woe was underlined when they were knocked out of the first round of the Scottish Communities League Cup yesterday after losing 2-1 to Forfar Athletic in extra-time.
The boardroom battle intensified after a group of shareholders and Scots billionaire entrepreneur Jim McColl had gone public with a plan to remove chief executive Craig Mather, financial director Brian Stockbridge and non-executive director Bryan Smart from the board.
The rivals instead want former Ibrox director Paul Murray and Frank Blin, a leading financial expert and former chief at accountancy firm PricewaterhouseCoopers Scotland, to be on the board.
Mather condemned the arrogance of the group behind the proposal.
Tensions ran high during yesterday's game at Station Park, which was played against a backdrop of public bickering and uncertainty.
When the winning goal was scored, a Rangers fan turned on Mather, telling him to get out of the club and "take your pal Green with you".
After the match McCoist said he was appalled by Green's comments over the club's future.
He said: "The self-acclaimed, straight-talking Yorkshireman has again let himself down.
"His contempt and total lack of respect for my players, for our football club, for our support and Scottish football in general is appalling - and he is an embarrassment."
The club announced on Friday that the board had appointed Green, who was forced to step down as chief executive over claims he was linked with ex-owner Craig Whyte, to the new post. It was a compromised decision because Green, the club's biggest individual shareholder, had originally wanted to be back on the board.
The latest boardroom drama to engulf the club has angered supporters, who say they want the turmoil surrounding Rangers to end and the focus to be on football.
In a lengthy statement yesterday, Mather said: "Again there are those attempting to bang down the doors simply because they feel they should be inside before any others and for no good reason other than self-gain and arrogance.
"It doesn't matter to them that they have not invested or helped the club, or that they failed to make even a remotely credible attempt to save this fantastic club in its darkest hours.
"Not a single one of them stepped forward willing to invest their own money. Yet now they think they can waltz into the club.
"This club needs commitment and unity.
"It does not require the type of people who stood back and did nothing when Rangers were in trouble. Now, as Rangers has been climbing on to more solid ground and as the fans are heartened by what they've seen, these men emerge from the shadows with empty promises.
"They should be ashamed. It is surely no coincidence that they waited until the signs are positive and strong."
A defiant Mather went on to say the club would not be defeated.
He added: "I certainly won't, and we will meet this latest ill-considered and ill-timed challenge head on."
Former Ibrox director Paul Murray led a failed bid by the Blue Knights consortium to save the company which owned the club after it plunged into administration last year. He teamed up with businessman Brian Kennedy to submit a takeover offer conditional on the acceptance of a Company Voluntary Agreement (CVA), before pulling out when creditors refused to agree to a CVA.
It is understood that Walter Smith, chairman of the club, is likely to back the bid by the shareholders and McColl.
The rebel group are calling for an Extraordinary General Meeting (EGM) to be held.
Green came back on board with the club as the bid was tabled "to promote the interests of Rangers" and will "assist with shareholder relations".
Support among fans is divided, with concerns being raised over the interests of those fighting for power at the top.
Drew Roberton, general secretary of the Rangers Supporters Association, said: "It's difficult to say what would be best for the club because we can't see the hard facts and figures.
"There will be a lot of divided opinions from fans but the united view is that we want the club to settle down and only people who are interested in the club - not their own jobs or status - should be on board.
"Rangers are making headlines for the wrong reasons yet again. When will this end?
"We've gone through enough. Everybody needs to work together for the common interest of the club which is to get back up to the top where we belong."
Mather, 42, was made permanent chief executive at the club in June after Green, 60, left the post.
The club raised £22.2 million under Green and he is the biggest individual shareholder in Rangers International with a 7.7% stake in the firm.
Rangers are verifying the latest bid by the shareholders.
A statement from the club read: "The Board of Rangers confirms that, on 1 August 2013, it received a notice requisitioning a General Meeting of shareholders.
"The requisition puts forward resolutions for the removal of Craig Mather, Brian Stockbridge and Bryan Smart as directors of the company and the appointment of Paul Murray and Frank Blin as directors of the company.
"The board is verifying whether the requisition is properly constituted and further announcements will be made as appropriate."