The Light Blues boss hit out after Green - who is set to return to Ibrox in a consultancy role - warned the manager in a newspaper article that he must win a cup this year and that simply delivering another league title would not be enough.
Hours later, Rangers crashed out of the first round of the Scottish League Cup 2-1 after extra-time to Forfar.
Speaking afterwards at Station Park, when asked for his thoughts on Green's remarks, McCoist said: "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."
On Green's cup claims, McCoist added: "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."
Green quit as chief executive in April but, in a statement to the London Stock Exchange yesterday, the club confirmed his return as a consultant.
And McCoist, who was unhappy with Green branding his players "the worst Rangers team ever" last season, made it clear he did not welcome the Yorkshireman's return.
He said: "After I've given him that endorsement it would be crazy of me to say 'welcome back Charles'.
"I've got to be careful because Forfar deserved their win and well done to Dick Campbell and his players.
"But our players picked up the newspaper at breakfast to be reminded they're the worst team in Rangers' history.
"I'll tell you, that would be bad luck - to have the worst Rangers team in history and the worst chief executive in history at the same time. That's downright bad luck.
"Instead of concentrating on the match, their minds are elsewhere and they're worrying about their jobs. Because, let's face it, if he's said we don't win a cup and we go, then some of the players would be under threat too.
"As team-talks go, I don't think it was one of Charles' best."
The match was played against a backdrop of fresh off-field turmoil, with a group of shareholders aiming to see the removal of key board members, including new chief executive Craig Mather.
McCoist said: "That's something I can't legislate for and don't have any control over.
"What I can say is that the current chief executive has backed us with players coming in, absolutely.
"Craig Mather has been shoulder-to-shoulder with us, which is something Charles seems to have taken umbrage to.
"Let's be honest about it, I don't think it's surprising that we're probably at our most vulnerable and weakest because we can't play our new signings [due to a transfer embargo].
"That's when Charles has surfaced and the biggest thing of the lot is that he's turned up after 34,000 fans have bought season tickets.
"Coincidence? Perhaps not."