Little returned from international duty with a suspected stress fracture to his foot and is likely to miss a number of weeks.
Greek full back Argyriou has a hamstring strain and will certainly miss Saturday’s match and remains a doubt for Tuesday’s clash with Queen of the South at Ibrox.
With four games in eleven days to contend with McCoist is hoping the remainder of his squad can cope.
He said: “Andy Little unfortunately is in a cast for a foot injury and will be for a couple of weeks, which isn’t good.
“He was away with Northern Ireland and he got a scan over in Belfast and it showed that something wasn’t right so we got another scan when he came back.
“They decided to put him in a boot. I don’t think it’s broken but there’s a possibility of a wee stress fracture.
“Anestis Argyriou has a hamstring injury so he won’t be involved tomorrow either.
“We’re a little bit bare on the ground and there’s two away. It's a tougher period in terms of the congestion of the games and we'll have to monitor them as they come up.
“It would be ideal to give some boys the chance to play but obviously circumstances will dictate that.
“With the two boys being out for certainly tomorrow, and Andy for the foreseeable future, I’m not saying we’re down to the bare bones I wouldn’t imagine there will be too many changes in personnel over the three or four games.”