Rangers will meet St Johnstone at Hampden next Sunday for a place in the final after Thistle were sunk by goals from Nacho Novo and Chris Burke.
"The result was always going to be more important than the performance," added McCoist.
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"There's always a bit of a worry when you come to a place like this.
"But I thought, over the 90 minutes, we deserved the win."
Steven Smith made his return after a 16-month absence through injury and McCoist was delighted to see the defender back in action.
"I'm really pleased he came through it," he said.
"I can relate to Stevie's situation because I was out for a long time injured and it's hard to deal with."
Smith was one of seven changes in the Rangers team as a few players were rested ahead of Wednesday's SPL visit to Celtic Park.
"Gone are the days of winning titles with a small group," continued McCoist. "It really is a 24-man squad effort."
Rangers travel across Glasgow with a four point advantage, having played two games less than Celtic.
Looking ahead to the next Old Firm clash, the former Scotland striker said: "Celtic's home record is absolutely fabulous - they are very strong.
"We know Celtic will come right at us. They are a bit like a wounded animal, if you like.
"If we go there and win it will put a serious dent in their title hopes and that's what we aim to do."