After a goalless 90 minutes, substitute Daniel McBreen put Saints ahead early in extra-time but Rangers equalised through Nacho Novo's penalty.
"Anybody who takes any credit from today's game must be St Johnstone," McCoist told BBC Scotland. "I thought they were terrific. I've got a lot of sympathy for them to go out on penalties.
"But from our perspective I'm thrilled to be in the final. We're a better team than we showed today. I'm really disappointed with our performance but genuinely pleased we're through to the final."