The League One champions head into their game with Raith Rovers aiming to lift their second silverware of the season after their romp to the title.
McCoist has had to contend with a host of off-field problems in recent years with Rangers' financial and boardroom troubles.
Now the Light Blues boss is pleased to concentrate on matters on the pitch.
He said: "This was all I had as a player and assistant manager. So it is good to get back to that level of pressure in football terms.
"I've been lucky to be involved in more cup finals than most. You tend to remember the ones you don't win more than the ones you do.
"It's great to get that feeling and that anticipation back again. That would indicate how seriously we are taking the competition.
"This is a great form of pressure. This is the pressure you want as a manager or player.
"If not enjoyable pressure, it is pressure you can understand, accept and appreciate, far better than the pressure of administration, liquidation and all that stuff."
While Rangers have racked up results this season, there have been grumbles about their style, but McCoist says the result is what matters tomorrow.
He said: "We need to win the cup, that's what we need to do. The last two weeks hasn't been fast, free-flowing football, but we won the games as well, which shouldn't be dismissed."
He added: "If you ask the Raith Rovers boys or supporters would they rather win the cup or would they rather see their team play fast, free-flowing football and losing the cup, I know which one they'd pick."