The Ibrox side fell to an embarrassing defeat to bottom-of-the-table Stirling Albion at the weekend and sit third in the Scottish Third Division, yet to win an away game this term
Stirling, whose manager was absent from the game on Saturday in order to attend his own wedding, capitalised on poor Gers defending to score the game's only goal.
The Beanos climbed off the bottom of the table with the win, while Rangers sit third and are yet to win an away game so far this term.
"There is no chance of Ally being sacked," Green told The Scottish Sun. "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. Ally will be the first to accept that he picked the team. That it 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."
The Gers have also only managed to win three of their six games at Ibrox this term, but beat Motherwell in the Scottish League Cup, making the league struggles doubly frustrating for Green.
He added: "I find it incomprehensible that the same players can win so well against top of the [Scottish Premier League] Motherwell and then play like we did at Stirling.
"We’re all frustrated, none more so than Ally — someone who knows exactly the privilege and pleasure it is to pull on a Rangers jersey and do it justice.
"Ally has absolutely my 100 per cent backing."