And he has urged the Light Blues supporters desperate to see change at boardroom level to remain firmly behind his team in the weeks ahead.
McCoist was grateful the Gers faithful did not turn on his players after they fell 3-1 behind against Brechin City at Glebe Park last weekend.
The Rangers manager felt their attitude helped to ensure the SPFL League One leaders staged a thrilling comeback and triumphed 4-3.
He is optimistic Rangers followers will continue to show unstinting support no matter what happens off the pitch in the remainder of the 2013/14 campaign.
"I know there has been a meeting this week with fans and potential board members," he said.
"But I don't know anything about it, I haven't spoken to anyone about it, it's not my business.
"All I can say is the fans have been brilliant. They're one of the main reasons we got ourselves out of a hole last week because we were toiling.
"Defensively, we were all over the place last week. And the fans would have been well within their rights to turn around and have a go. But they didn't."
McCoist added: "I keep saying we need to get a bit of stability for the fans. That's what they deserve, that's what they want and hopefully that is what they'll get.
"Whatever else has been going on, they've been 100% focused in their support of the team. It's amazing.
"The amount of people who have said to me, not even begrudgingly, how amazing it is.
"Supporters of other clubs freely tell me that they've got a huge amount of respect for the way our fans stuck by this club, supporting the team and the club.
"I don't see it changing because they're intelligent enough to know the long-term situation with regard to the team isn't an overnight fix. Far from it.
"They know that and they've shown incredible patience. I believe that will continue."
Despite unhappiness at his side's slipshod defending against Brechin, McCoist was pleased with the spirit they showed up in Angus.
He is hopeful his charges will have learned lessons from their disastrous first-half display and perform far better in future - starting against East Fife in Methil this afternoon.
He also feels, despite admitting his squad will need strengthened significantly before Rangers return to the top flight, that his players have long-term futures at Ibrox.
"I'm loathe to say they will learn from their mistakes because it could come back and bite me on the backside," he said.
"But I couldn't have been happier with the spirit we showed in the second half. I just hope the performance level in our defending was a bit of a one-off.
"We won the game - which we were delighted with - but looking at the bigger picture, we were all over the place defensively.
"We looked like we were going to score goals and thankfully that's what got us out of a hole. Our ability to defend wasn't nearly as good as our ability to score goals last week."
McCoist continued: "Time will tell who makes the journey. But there are players here capable of going every step of the way with us.
"There has been a massive improvement - but there is still more improvement to come.
"I think it's safe to say you can see a massive improvement from last year. But we've still got a way to go.
"We will have to improve next year, and the year after that again. And there is improvement in the players we've got, the players we've brought in.'
McCoist has been a key figure in the ongoing saga at Rangers in the last few years and would have an instant bestseller on his hands if he ever decided to recount his experiences in a book.
But in the week Sir Alex Ferguson released his explosive new autobiogrpahy, he stressed he would not be going down that route.
"Oh I wouldn't have thought so," he said. "With the greatest of respect to Sir Alex, nobody would believe mine!
"It would be in a completely different shelf! Comedy, horror, it could be a little bit of everything."