Second-half goals from David Templeton and Andy Little secured the win against the bottom side, who inflicted Rangers' only league defeat this season at Forthbank in October.
McCoist said: "I was a little bit concerned, with the way things were shaping up, that we would end up with a damp squid and the result not going our way. I'm mightily relieved and pleased with today."
The match attracted an impressive crowd of 49,913 - a record for Ibrox this season. The manager added: "It's absolutely amazing. I've been sitting here for weeks saying to you guys just how difficult it is to comprehend. The occasion was fantastic for everybody involved with the club."
Goalscorer Templeton made his first start since suffering ankle ligament damage in mid-September and the winger found himself the victim of challenges which earned four Stirling players yellow cards in the opening 35 minutes, including Daly McSorley, who was dismissed by referee Mike Tumilty late on.
McCoist said: "You have to say that we're all in the hands of the referee's interpretation of the laws. I would probably say he got all of the decisions correct.
"Unfortunately, the way Temps plays the game, he's going to draw attention from players. He lulls defenders into situations where they are going to have to tackle him.
"As long as the fouls on him are mis-timed, rather than anything else, I don't have a problem with it. It's part of the game. I was delighted with the way he got back up and took the ball again. It's testament to him after a few hefty slaps that he still wants to take the ball and commit defenders."
Asked for his opinion on the referee's performance, Stirling boss Greig McDonald said: "Mike is probably the best we've got, I think he's a cracking referee. I think he made his job a wee bit harder when he gave five cards for the first five fouls.
"The tempo was set in the first minute when Marc McCulloch made one of the best tackles I've ever seen and got booked for it. He clearly got the ball, but it looks spectacular because the Rangers player went about six foot in the air. I've no real complaints about the sending off."
- Sports & Recreation
- David Templeton