The former Hearts defender curled home an 87th-minute winner with the outside of his boot to earn Saints a 2-1 win (2-2 aggregate draw) on Thursday night.
But Saints paid the price for losing a sloppy goal in the 74th minute against the 10 men from Armenia.
Michael O’Halloran’s powerful strike gave Tommy Wright’s men a first-half lead and the tie looked to be turning in the Scottish side’s favour when the visitors’ Karen Muradyan was sent off after the break.
But Norayr Gyozalyan lobbed Alan Mannus after a long ball went straight through the heart of the home defence.
McKay could not celebrate his goal as Saints missed out on a trip to Kazakhstan.
“I wish it had been the one that put us through but it wasn’t to be,” he told the club’s YouTube channel. “That spoils it. We had a bit of pressure after that but it just wouldn’t fall to anyone at the end.
“It’s heartbreaking, putting so much effort into it and the travelling as well.
“We are desperately disappointed. With them going down to 10 men, you would think we go at least to extra-time. We made it difficult for ourselves by conceding a sloppy goal.
“There’s no hiding behind that, we shouldn’t concede a goal like that. It was just a long ball up the park and we have not dealt with it.”
Saints boss Tommy Wright’s problems did not end with the defeat as he was left facing even more injury problems.
St Johnstone were missing an entire midfield after Simon Lappin and David Wotherspoon suffered ankle injuries in training after Chris Millar (hamstring) sat out the trip to Armenia and Murray Davidson sustained a knee injury in the first leg that will rule him out for several months.
And centre-backs Frazer Wright and Steven Anderson both went off injured at McDiarmid Park, the latter with a suspected cheekbone fracture, joining Dave Mackay on the sidelines following his hip surgery.