Reports this week suggested a rift between chief executive Charles Green and chairman Malcolm Murray.
But McCoist says dealing with rumours of a spat behind the scenes is tame in comparison to the trauma Rangers have endured over the last 12 months.
He said: "It's not been unsettling at all, to be honest with you. It's part and parcel.
"In comparison to some of the things that have been going on, it's quite mild, believe me.
"I know all the members of the board and they all want Rangers to improve and head in a positive direction.
"Everybody within that boardroom wants the same thing and I'm encouraged by that."
Green's consortium seized control of the club in the summer after liquidation was confirmed.
McCoist added: "Since the takeover, in my opinion, there has been a real positivity. None more so than from the supporters.
"From the people within the club - the staff, players and support-base - I genuinely get a really good feeling about the club and its attempts to get back to where we want to be and should be. Everybody is pulling together.
"There will be steps back, there is no doubt about that, but the main thing is that we all remain united and that will be case."
Stock market rules prevent McCoist from going into detail about events in the boardroom but he is confident everyone involved in the running of the club has the best interests of Rangers at heart.
He said: "Having been to certainly one board meeting, where I've met all the members of the board, there is absolutely no doubt in my mind that every member of the board is going in the same direction and has the same wishes and hopes and desires and plans for the football club.
"Within any boardroom and any business, there will be differences of opinion. Of course there is. That would only be healthy in my opinion.
"I can reassure every Rangers fan that everybody within our board is going in the same direction in terms of wanting the club to move forward."
He added: "I have gone on record as saying that I believe an openness and a frankness and an honesty within the club is of paramount importance to everybody - supporters and staff alike.
"There will be issues that must remain in-school but our fans deserve to know what's going on within the club and I don't have a problem with that at all.
"I can reassure them that everybody to a man is behind the club going forward and we are all united in the efforts to move the club forward."
Green this week said that Rangers had settled their outstanding football debts after Hearts accepted a final instalment of £400,000 for Lee Wallace, while Rapid Vienna also received a fee for former striker Nikica Jelavic.
McCoist said: "It's important because we are a very proud club, with a proud and great history, and we are proud of the fact that we attempt to do things the right way.
"Of course, sometimes we will get it wrong. But it is important to us, as staff and fans of the club, that we do the things that seem to be right.
"We've always had great standards and we want to retain them."
Meanwhile, Lee McCulloch is set to remain on the sidelines in Saturday's Third Division clash at Berwick.
The Gers skipper has consulted a specialist over an ongoing ankle problem and, although no timescale has been given for his return, McCoist hopes he will play again this season.
He said: "It's been really tough for the big fellow.
"He went to see a specialist on Tuesday, who has given his opinion on it and we're hopeful that progress will now be made.
"It's been a lot longer than Lee would have hoped for and we would have hoped for.
"We can't put a specific time on it but I would certainly hope he would play again this season."