The Parkhead team was seen by most, including McCoist, as the most likely to win the trophy going into the fifth round.
But Neil Lennon's side's surprise 2-1 home defeat to Aberdeen has blown the tournament wide open and Gers have been installed by some as the new front-runners.
McCoist has always believed the Light Blues can be bracketed in a category with some of the more prominent Premiership sides in terms of being cup hopefuls.
Yet he maintains the likes of Dundee United and the Dons - two sides which have impressed in the top flight this season - are probably still ahead of his squad on that front.
He has also picked out his former club St Johnstone as a team to be wary of after their emphatic 4-0 win at Forfar on Saturday.
McCoist said: "Some bookies might have us as favourites now as is their right, but I wouldn't go that far.
"I'm not trying to play any mind games when I say this but I think Aberdeen and Dundee United will, in a lot of people's eyes, still have a slightly better chance.
"I counted us in the next band after Celtic and I still do. I don't think there's an awful lot between a lot of the teams there.
"But United beat St Mirren 2-1 on Sunday and I watched St Johnstone three weeks ago when they beat Partick Thistle 1-0 and they weren't looking bad at all.
"You've got to say they had a fantastic result at Forfar and a lot of people would have been looking at that as a really tough fixture.
"We're in the mix but when you consider the other teams in there, I still don't think we're favourites to win the competition. I genuinely don't.
"You'd have to say Aberdeen, having knocked the holders and the champions out, would probably be most people's favourites now."
Rangers were drawn to host Albion Rovers in the quarter-finals of the tournament and it's a tie the League One leaders will be expected to win.
They beat the Coatbridge side 4-0 last July in the opening round of the Ramsdens Cup at Livingston and were very comfortable that afternoon.
But just as Gers have yet to concede a goal in the competition, the same applies to James Ward's side.
On their way to the last eight, Rovers have enjoyed 1-0 victories against Spartans, Deveronvale and Motherwell before a 2-0 success against Stenhousemuir.
The chance to advance to the last four where both ties are being played at Ibrox is undoubtedly attractive for McCoist.
But the Light Blues manager has staunchly reiterated he and his players will take nothing for granted when they face the Cliftonhill team next month.
McCoist added on the official Rangers website: "I'm just delighted to be there. We all are and what an incentive it is for us to have as we try to earn a semi-final against someone at Ibrox.
"We have a fantastic opportunity to continue our run and that's all I'd say it is. We can't look any further than the next game, where it's a no-lose situation for Albion Rovers.
"They'll come to our place and a lot of people outside our club will fancy us to win quite comfortably as we've already beaten them, but we won't be thinking like that at all."