The club's board held a meeting to discuss revelations involving chief executive Green, commercial director Imran Ahmad and Craig Whyte, who owned Rangers before the club was liquidated.
Supporters chanted "Charlie, Charlie give us the truth" as the Third Division winners beat Clyde 2-0.
Asked whether the fans have changed their views on Green, the Rangers manager said: "I don't sense that they are turning away from anything or anybody.
"But I do sense, quite rightly, that they are getting a little bit frustrated that the whole thing isn't out in the open, that the truth isn't there for everybody to see - especially the Rangers supporters.
"They deserve the truth. They deserve to know what's been happening behind the scenes at their club.
"I do detect a greater frustration from within them and I do understand it and, I take it a step further, I agree with it."