Rangers suffered arguably the worst defeat in the Glasgow club's history after going down 1-0 to Stirling Albion at Forthbank in the Scottish Third Division on Saturday.
Rangers were forced to start life again as a newco after being liquidated in the summer, but have made heavy weather of life in the bottom rung of Scottish football despite being expected to dominate.
They have yet to win an away game in the division having been held to draws with Peterhead, Berwick Rangers and Annan Athletic. They have also been knocked out of the Scottish Challenge Cup by Queen of the South at the quarter-final stage.
“There is no chance of Ally being sacked. Yes, Saturday’s defeat was an embarrassment. But no one more than Ally knows what happened at Stirling was unacceptable," said Green.
“We’ve got to get a lot of things sorted at the club and we’ve never said it was going to be easy. We are certainly not going to solve anything by dismissing the manager.
“Remember, the manager wasn’t on the field on Saturday, was he? Ally will be the first to accept that he picked the team.
"That is his responsibility. But no matter the players picked, Rangers should still be able to put out a team to beat anyone at this level.”
Rangers are one point behind leaders Peterhead and Queens Park in the table after seven matches with their next match against Queens Park at Ibrox on October 20.
"We’ve got a fortnight now until our next game and that gives us all time to take stock, reflect and plan ahead.”