Substitute Fraser Aird scored in the dying seconds to ensure McCoist's first trip to Hampden Park as manager ended in victory.
And McCoist also had empathy with opposition manager Gardner Speirs, whose side finished the game with 10 men after James Brough was dismissed on a second yellow card.
McCoist said: "Of course I have sympathy. Gardner is a good lad. His team gives him absolutely everything and I'm sure you will agree they were really well organised.
"They probably had their better opportunities when we were a bit reckless in pushing forward. It would need to be a cruel man who didn't have any degree of sympathy for the opposition.
"At the same time, I've got to look after our own corner and I'm thrilled with the victory. It was a relief.
"To be honest, I think we lost our shape a little bit a couple of times late on in pursuit of a goal, which is inexcusable.
"I can understand the desire to get a goal but we should have been more solid."