The defeat was the Glasgow club's first defeat since they were demoted to the Scottish Third Division but Green has insisted that there is "no chance" of McCoist being dismissed as manager.
Green told The Scotsman: "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.
"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."
Rangers are currently third in the Scottish Third Division table.