The Yorkshireman was given a new consultancy role at Ibrox last week and marked his return with some frank views on the state of the Scottish League One club.
Green said McCoist's team should be challenging for a cup as well as promotion this season, and the Rangers boss called the comments "embarrassing" and blamed them on contributing to the 2-1 League Cup exit at Forfar.
That public spat was followed by the exit of non-executive chairman Walter Smith from Ibrox, and McCoist tried to focus on his relationship with chief executive Craig Mather on Friday following another week of turmoil in Govan.
McCoist said: "I made my views, I would have thought, crystal clear last Saturday - and that's all I've got to say on it really now, I just want to go on about football.
"I've got nothing to do with what action the club or the board will take. They'll do what they see fit on that. As I said, I did make my views quite clear at the time what I thought about the comments.
"I think Charles is a shareholder now. So there is no real reason for me to talk to Charles.
"I'll certainly talk to the most important man just now at the moment is absolutely Craig Mather, who has absolutely helped me bring players in - and Craig has been absolutely first class with that.
"That is a relationship that has been very, very good and very beneficial to me, and hopefully that can progress."