The 20-year-old sat on the bench as the Hoops raced into a 5-0 interval lead to kill off any Gorgie hopes of cup glory.
McKay was asked by boss Gary Locke to go on at the start of the second half to help stem the tide and was partially successful as the game ended 7-0 for the rampant visitors.
Ahead of the Scottish Premiership clash with Neil Lennon's side at Celtic Park on Saturday, McKay recalled Hearts' humiliation with regret rather than relief.
He said: "Obviously you don't want to be getting beat but you don't want to sit aside and see your team getting beat like that.
"You wish you could do something about it, you wish you were on there, helping the boys and talking to them, organising them, which I like to do.
"I would never sit aside and say I wish I wasn't playing or glad that I wasn't playing. Never.
"The game was over when I got on, 5-0 at half-time is never great.
"Celtic were playing some unbelievable stuff and I was on the bench watching it, puffing my cheeks wondering what was happening.
"I came on and was told first and foremost to defend. We had tried to have a go at Celtic and it wasn't the right thing to do, the way they were playing.
"They exploited gaps and punished us.
"The second half was a wee bit easier because we sat in and soaked up the pressure and conceded a penalty and an unlucky deflection.
"If we had done that in the first half, maybe it wouldn't have been so bad."
The administration-hit Gorgie club - docked 15 points and barred from signing new players - are stuck at the bottom of the table on minus three points, 14 behind second-bottom Ross County.
However, McKay believes they can take something from the table-toppers who are looking to go 16 league games unbeaten.,
"Anything is possible," he said. "I have never played at Celtic Park but I have been on the bench and I know what the atmosphere is like and I know what we have to do.
"Everyone I speak to says, 'Celtic Park, you are going to get hammered, what are you thinking?'
"It is a difficult place to go - it is difficult for Barcelona.
"But I think it is a great opportunity. There will be a lot of people watching and it is going to be on the telly, so I am excited about it, it is a great prospect for the young boys."