The champions eased into the next round thanks to a Dean Shiels hat-trick and superb solo effort from David Templeton against their League One rivals.
McCoist's side will discover their quarter-final opponents tomorrow afternoon when the draw is made and the Ibrox gaffer was delighted with a top showing from the Light Blues.
He said: "I thought it was a great 90 minutes, we were solid throughout the whole match and there were some terrific individual performances. Overall, it was a really good team performance.
"The first goal was a good strikers goal. Dean used his backside to get a half yard and nudge the boy and it was a good finish.
"The second goal was similar and the third one was a good finish as well after a good move down the left hand side.
"He is certainly chipping in, not just with a good level of performance but some important goals for us.
"I have said before, to be fair to Dean, and Temps, who played really well, both of them didn't get the full pre-season through injury and they have struggled at times to maintain a good level of fitness. They have had injuries here and there.
"I don't have any doubt that when they are fit and available for selection that they are more than capable of turning in the sort of performances than you saw last night.
"It is a boost for everybody to get into the quarter-finals.
"It is the showpiece tournament and we want to give the fans something to look forward to."