Derek McInnes voiced his displeasure after the match at the antics of right-back Mikael Lustig, who celebrated in the face of Lewis Ferguson shortly before the full-time whistle.
Several players confronted the Swedish international for his apparent goading of the 17-year-old as Celtic got their hands on the first domestic silverware of the season with a 1-0 win.
Shinnie insists the Betfred Cup winners should have been a bit more humble in victory.
He said: “It just frustrated me when some of their players are celebrating in front of a young 19-year-old kid who is just trying to do well. You can have a wee bit more class than that.
“There’s ways to go about being a captain. You can have a bit of class about you - they don’t and it frustrated me. But we have to deal with it. They were 1-0 up and they had the ascendancy and it gave them the chance to do it. I’m big enough and man enough to take it.
“He will do what he does. It doesn’t bother me. But when it’s people like young Ferguson they are going for...they are older professionals and they should know better. But we can deal with it.
“Did I have to speak with Lewis afterwards? No, he’s a mature young man.
“He’s dealt with stuff like that in the past and he will deal with it again when he’s involved in big games. He can handle himself very well and he will be fine.”