McCoist's men have been drawn to play SPFL League Two part-timers Albion Rovers at Ibrox in the quarter-finals of the competition next month.
And if they overcome the Coatbridge club, who are in the last eight for the first time in 80 years, they will play at home in the semi-finals.
Some bookmakers have made Rangers favourites to win ahead of Premiership high-flyers Aberdeen.
But the Dons beat Celtic 2-1 at Parkhead on Saturday and McCoist believes they are more likely to triumph.
Speaking to the official Rangers website, he 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 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.
"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."
McCoist also feels Dundee United and St Johnstone, who defeated St Mirren and Forfar respectively, have a good chance of triumphing.
He said: "United beat St Mirren 2-1 and I watched St Johnstone three weeks ago when they beat Partick 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."