The 21-year-old was handed his first cap by Gordon Strachan during Saturday’s 3-0 defeat by France.
It topped off a breakthrough campaign for the Murray Park graduate which also saw him named Rangers’ young player of the year.
McKay knows he is far from the finished article but hopes hard work will ensure he gets better and better.
He told the Rangers website: “You can always improve. I am sure the players we played against would say the same, they would say that they have still got a long way to go. Quite a few of them are still quite young, they are my age or even younger than me.
“The manager said to go and enjoy it and try to get involved as much as you can. That was it really. He just said to go on and enjoy the occasion.
“I would love to play for my country again. I have always said that, even if it is at under-21 level or first-team level. I would just love to play.”
McKay – who played 48 times for Rangers over the season, scoring nine goals – came on for the final nine minutes of the clash in Metz.
While it was a disappointing evening for the Scots, McKay showed some bright touches and admits he will cherish the memories of his introduction to international football.
He said: “It was the first cap for my country at first-team level. I came up through the youth system in Scotland, so to be able to make my first-team debut was a proud moment for me.
“Unfortunately, the result wasn’t what we wanted. That would have made it an even more special occasion for myself.
“I think I did OK playing against one of the best teams, if not the best team, in Europe.
“It was always going to be hard to get a few touches on the ball, but I did do it.”