The Light Blues have been made favourites by some to lift the silverware come the end of the campaign as they look to add a cup double to the League One crown they are likely to wrap up by the end of the month.
Giant-killing Albion Rovers stand in the champions' way on Sunday afternoon as James Ward's side aim for another scalp after knocking out Motherwell and Stenhousemuir in the previous two rounds.
And McCoist is determined to make the most of the Gers' opportunity and keep their Treble dreams alive.
He said: "It's a fantastic incentive for the players but it would be a fantastic boost for the supporters and everyone connected to the club to get back playing in a cup semi-final at a major stadium.
"But we are not underestimating the task. In the Scottish Cup the Albion Rovers players are doing something right.
"I hope the players sense how special this could be. I don't want them to be up there and get too carried away. But I do sense the anticipation.
"Rightly or wrongly people look at us and see that we are going to win the league and secure promotion.
"There is a big question mark is do we have the luck, the ability and the potential to go far in the cup.
"We've done that and now we have a terrific opportunity to get to a semi-final. I was hoping we'd get a run in the cup because it would give everyone a boost.
"But I stand by what I said at the start, getting out every division we are in remains the priority.
"There is absolutely no doubt the staff, players and supporters would get a boost from a cup run."