Goalkeeper Steve Simonsen had a shocker between the sticks and the Gers blew numerous goalscoring opportunities, but McCoist insists that the entire team must shoulder responsibility.
"I didn't speak to anyone individually. I spoke to all the boys," McCoist told reporters. "Every one of them is disappointed.
"It would be unfair and wrong of the me to single anyone out for errors. We missed chances and we gifted one or two goals. You win and lose as a team, although of course they were individual errors."
United will play either Aberdeen or St Johnstone in the final.