Greenock businessman Easdale has stated the Ibrox club could "be pulled apart" if fans carry out their threat to withold season ticket money.
McCoist has refused to get drawn into the stand-off between a section of Gers supporters and the board this season.
But the manager, whose players will be presented with the SPFL League One trophy after the game against Stranraer tomorrow, was alarmed to read Easdale's comments.
He said: "It is obviously a concern. The livelihoods of the staff at the club are the most important thing.
"The future and health of the club are of vital importance, but without doubt the people within the football club and their livelihoods are extremely important."
Meanwhile, McCoist has urged his charges to celebrate their third-tier success fully after the penultimate game of the 2013/14 campaign tomorrow. He said: "I read one ex-player say a few weeks ago that we had a cheek to celebrate it.
"I did find it rather amusing because he would have been the very same player who would have torn us to ribbons had we not celebrated it.
"No, we have to do it justice and do the right thing, and that is celebrate the title success.
"The players deserve enormous credit for their league campaign. I think any level-headed person would see that."
Rangers fans are set to stage further protests at the final home game of the season - but McCoist is confident they will show their backing for the team.
He said: "Our supporters have been through hell. But the vast majority of them all appreciate the fact that we have won the league and won the league well and I would expect them to celebrate and enjoy their day."