Jon Daly grabbed the only goal of the game in Tuesday's last-four clash against Stenhousemuir to book a final date with Raith Rovers in April.
McCoist said: "It means everything to us all to be in the final. It's part of the process back to where we want to be. We haven't been in a final for a long, long time.
"There was certainly nobody within our club who was underestimating how important it was for us to get there.
"It's a great day out and it gives the players and the staff the opportunity to go to a final. More importantly, it gives the supporters a big day out.
"If anybody needed a big thank you and a day out it's our supporters so it's great.
"It was just as difficult a game as I thought it was going to be. Until you get the first goal you are alway concerned.
"In that respect, it was as hard as we thought it would be. I don't think in the grand scheme of things that anybody could grudge us the victory.
"We hit the crossbar three times and we thought we might have had a penalty."
Stenhousemuir boss Martyn Corrigan said: "The game plan worked a treat and we created a few opportunities. It's just unfortunate we didn't take them.
"The boys were excellent. I was disappointed that a Stenhousemuir player didn't get man of the match.
"On another day, we might have been in the final. We didn't perform well at Ibrox (8-0 defeat) and this game shows how far we have come."