With tensions between the Ibrox terraces and boardroom at an all-time high, around 16,000 punters have decided not to hand over their cash ahead of the new Championship campaign.
While some supporters will not be back while the current board is in place, many are likely to pay on a game-by-game basis as McCoist's side look to clinch their return to Scotland's top flight.
Only 18,000 turned up to see the Gers beat Hibernian in the first round of the Petrofac Training Cup on Tuesday night, but McCoist is expecting a far bigger turnout for the visit of Hearts tomorrow.
He said: "I think we will get a good crowd, though I have no idea right now how many. I thought we had a good crowd on Tuesday for a game which was live on television.
"I thought it was a reasonable crowd and I don't see our support not coming out in big numbers, particularly for this game. The one thing our supporters do is respect and honour their heroes very well.
"I fully expect a healthy attendance. We need the support as much as we ever have. No-one is more respectful of and thankful for the support we've had in the last couple of years.
"We will need it again this year more than anything because it's going to be tough.
"There will be games where the players will have to dig deep and there is no better way to dig deep than when you have the supporters with you."
The visit of the Jambos is a blockbuster start to what is set to be a campaign to remember as Rangers battle it out with their Capital counterparts for the title.
The Gers were far from convincing as they required extra-time to beat Alan Stubbs' side, but McCoist can't wait to get down to league business as old rivalries and acquaintances are renewed this afternoon.
He said: "You'd hope [we are up for it], along with Ian Black, Lee Wallace, which they are. We're really, really looking forward to it.
"Tuesday was a great start in terms of the results, but for a balance, Hibs were very good for a spell in the second half when we weren't that clever at all and didn't have the ball.
"But the results in cup ties are always the most important thing and it sets us up nicely for Sunday."