The Gers secured the trophy with a thrilling 3-2 victory over Queen of the South on Saturday to help them bounce back from the disappointment of missing out on the SPL title to Old Firm rivals Celtic.
Smith decided to give McCoist the responsibility of taking charge of the side for the Scottish Cup campaign and he feels it was good experience for him.
"I think he enjoyed the experience and it is good we went on and won it," Smith told Sky Sports News. "The culmination of winning was a big thing for him."
Despite giving McCoist extra responsibility for the successful run in the Scottish Cup, Smith insists he has no plans to leave his role as manager for some time yet.
"I am happy enough to be in my position and I don't want to leave it at the present moment," added Smith.