The 17-year-old terrorised the visiting defence with a series of surging runs and probing passes during the 3-0 win at Ibrox.
McCoist said of McKay: "I was delighted with the wee man.
"I thought his first-half performance lit up the stadium at times - really quick and direct and some of his general play belied his years."
The Gers manager was also pleased with Kevin Kyle, who scored one goal and set up another, saying: "Kevin got his first goal in the league the week before last. It was important that he continued with his form and his progress and I thought he did that.
"We've certainly got a young, inexperienced team. Five months ago they didn't know each other, let alone play with each other but I can see a natural progression and some of the play has been good."
McCoist played down talk of his side going all the way in the competition, but added: "I'd love a Cup run, that's for sure.
"I wouldn't start screaming from the roof-tops that we're ready for anything but an SPL team wouldn't scare us."