The Wales skipper, who joined the Toffees in a £12million deal from Swansea City, is eager to taste success in the latter stages of his career having been a great servant in South Wales but for little actual prosperity.
"I do look at football a little differently now having gone to the tournament and gone so deep into it," the 31-year-old said.
"What we achieved, Iceland too, and Leicester shows that with the right ingredients you can achieve anything really. Before Leicester, you probably thought certain teams would finish in certain places.
"I have tasted that. I'm not young, I'm not 21, so if I can in the last part of my career, I would like to try and sample that kind of atmosphere again.
"So I do look at things differently and it was nice. I want to be on the stage again at some point, whatever level that is I can get to.
"You can't go much further – maybe a World Cup or the Champions League I suppose."