McKay took advantage of some slack defending to give the hosts the lead on 10 minutes, before doubling his tally after an hour's play with a curling effort beyond goalkeeper Ben Williams.
Caley Thistle captain Richie Foran bagged the only other goal of the day as Butcher's side responded well to their Scottish Premiership defeat to Aberdeen last weekend.
The performance of his centre-forward, who was the subject of transfer interest from Bulgaria over the summer, caught the former England international's eye.
" We could have had more goals but the thing about Billy is, he misses one chance and it doesn't bother him," said Butcher.
"He will go and stick the next one in. He's terrific for us and he's now got nine goals for us this season and could easily have had a hat-trick.
"We had three players, Richie Foran, Aaron Doran and Gary Warren, that were on the edge of playing but passed fitness tests because they wanted to play.
"The lads really enjoy it here and make it difficult for the opposition. I asked them after the game what the difference was and they just said there is more freedom playing here. It was a beautiful day, a lovely surface and they knocked it about really well."
- Sports & Recreation
- Richie Foran
- Scottish Premiership