The League One club are expected to sweep aside Albion Rovers on Sunday, when the League Two club visit Ibrox for their quarter-final clash, live on Sky Sports.
McCoist's charges are considered a better bet to claim the trophy ahead of Dundee United, Inverness Caley, St Johnstone and Raith Rovers, with Aberdeen still the favourites after their victory over Celtic in the last round.
"It's difficult to gauge with cups because you do need the luck of the draw," McCoist said.
"Should we be amongst the favourites? I don't know. Dundee United look not bad while Aberdeen have beaten Celtic twice in the last four weeks.
"I don't look at it and think we are second or third favourites because, with the greatest of respect, nobody really knows how to gauge our team.
"Cup ties are one-off games anyway but because we are not playing at the top level no one really knows where we are it, so it doesn't really bother me what the bookies say."
Rovers have already claimed a big scalp this season when they beat Motherwell, and McCoist insists Rangers will not be underestimating the Lanarkshire team despite already beating them in their Ramsdens Cup showdown earlier in the season.
McCoist added: "It is no different in respect to Motherwell, who were favourites to beat Rovers when they played, as were Stenhousemuir. So that indicates that the favourites tag doesn't really matter.
"The fact that we are at home and have already beaten Rovers this season would indicate that we should be strong favourites. We just need to make sure that we deserve that tag by winning."
Watch Rangers take on Albion Rovers live on Sky Sports 1HD on Sunday, with coverage under way from 3pm.