Green, who is poised to return to Ibrox in a consultancy role, was quoted in the Saturday morning press as saying that McCoist needs to win a trophy in addition to the Scottish League One title this season.
"This year is a different year," Green told the Scottish Sun. "He has had a pre-season and he has been able to sign players.
"Ally has got to win the league - and got to win a cup. That's the stark reality of life. Ally is a fantastic guy. He is brilliant with the players, fans and media.
"But first and foremost, a manager has to win matches and has to win competitions. He knows he has to win the league and, in my opinion, has to win a cup as well. If he doesn't do that, he has a problem."
Within hours of Green's words going to print, Rangers' first chance of serious silverware disappeared as they were beaten 2-1 at Forfar after extra time.
After the match, when asked what he thought of Green's comments, McCoist told reporters: "I was appalled by them to be quite honest with you. 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.
"If it was a threat then the self-acclaimed straight-talking Yorkshireman should know that boys from the West of Scotland don't scare easily. If he does come back, I'll certainly go and pick him at the airport. I won't have a problem doing that. It's just more hot air that we've come to expect from Charles."
Rangers begin their league campaign at home to Brechin next Saturday.