The USA had a half-time lead, but surrendered that as Scotland scored four tries in the second half.
"That was fantastic - I'm so proud of my players," McCormack told BBC Sport.
"It was unbelievable. My players were written off at the beginning of the tournament and they have shown time after time what a fantastic bunch of players they are."
Despite the win, Scotland will only progress to the last eight if Italy fail to beat Tonga on Sunday.