Green - back at the club as a consultant - claimed in a newspaper article at the weekend that McCoist must win one of the cups, as well as the league title, this season.
The Light Blues boss then hit back with a sensational post-match verbal volley after watching his side crash out in the first round of the Scottish League Cup to Forfar on Saturday.
McCoist branded Green "an embarrassment" and criticised the timing of his remarks as his side prepared for the cup clash.
The pair already had a rocky relationship after Green last season labelled McCoist's players "the worst Rangers team in history".
Green told Sky Sports News: "I was chief executive, he was manager. We both did our jobs. It wasn't a great relationship and the whole world knows it.
"Let's be clear about where we are: This club has got the second biggest wage bill in Scotland. It's got the biggest history and reputation in Scotland, and the fans - quite rightly - expect better than what they saw last year.
"What I said - and I still stand by it - is that he's got to win the league and he needs to win a cup. Otherwise, we are not getting value for money.
"I didn't say it to put pressure on Ally and I didn't say it to put pressure on the players.
"I said it because that's what I believe. Anything less than that is not to the standards."
Green added: "I'm a problem to Ally McCoist, I'm a problem to the FA, I'm a problem to everybody because I say it how it is.
"I don't say it to be politically correct. I don't say things to make friends. I say it because it's correct."
Green made his return to Ibrox last night as Rangers were held to a 1-1 draw by Newcastle in a friendly.
He sat several rows away from McCoist in the directors box, before the manager took his usual spot in the dugout for the second half.
McCoist refused to discuss the spat with Green afterwards but did express his disappointment at Walter Smith's decision to resign as chairman.
Smith quit the post on Monday amid a bitter power struggle, which sees a group of shareholders aim to remove key figures from the board, including chief executive Craig Mather.
In a statement, Smith called for fans to get behind formal moves to install former newco director Paul Murray and Scottish accountant Frank Blin onto the board.
Asked for his reaction to Smith's departure, McCoist said: "I'm obviously very disappointed - that goes without saying. I'm very disappointed indeed."
Pushed on whether he had concerns that Smith's exit left him isolated, he added: "I don't really think so, to be honest with you.
"I don't think there is an awful lot more Walter could have done.
"He has got his own reasons for his departure. I respect that, totally respect it.
"Once again, there is no doubt it will be with the club's best interests at heart, whatever has forced him to make that decision."