Two goals from former striker Jonathan Walters steered Stoke to a 5-0 victory in Sunday's semi-final at Wembley. Matthew Etherington, Robert Huth and Kenwyne Jones were also on target as Tony Pulis' side ran amok.
Coyle said: "I will analyse it, as hurtful and horrible as it will be to watch it again. We have to learn from it."
He added: "Was the stage too much for one or two of them? Football is not just about physical ability. There is a mental strength that goes with it. I loved these occasions as a player.
"There were too many who didn't perform anywhere near to the right standard. We had a number of players who were at the bottom of the ladder. It was never going to be good enough against a very good side.
"The beauty of management is that you have to respond to things like this. You can do one of two things - you can pick yourself up and go again or you can hide.
"There is no getting away from the fact it was a below-par performance. Bizarrely enough, I thought we started the game reasonably well. But we were the architects of our own downfall."
Bolton captain Kevin Davies described their performance as "a terrible dream".
He said: "It was a horrible experience, the manner of the defeat. The first goal was like something from five-a-side rather than on an occasion like this.
"To see the goals going in, I don't know what to say. It was just one of those days. We will try to put it right. It is just a terrible dream at the minute."
Source: PA
Source: PA