The Light Blues have failed to win the lower- leagues competition in the last two seasons, losing to the eventual winners Queen of the South while they were in the Third Division, then to Raith Rovers in the final at Easter Road in April.
Rangers have major fitness doubts over Richard Foster, Ian Black and Kenny Miller ahead of their second-round tie at home to Clyde tonight but McCoist admitted: "It certainly would be a disappointment not to win it. Last season's final was disappointing because we had really good chances to score.
"That was as big a disappointment as anything we've had in recent times.
"The most important thing for us this season, though, is to get out of this league and get back up to the top flight.
"We need to get back to the position where, along with Celtic, there is an expectation that you will win cups.
"But we have a good bit to go before we are anywhere near that."