Arsenal won 2-0, with Dwight McNeil hitting the post for Everton.
Moyes said afterwards: “The block from Calafiori on Dwight McNeil is unbelievable. And it tells you a little bit about maybe the way Arsenal are. They're fighting for it, they're defending their goal with their lives.
“Probably in the end, I think, Raya made more saves than Jordan Pickford in the game. But the block from Calafiori was amazing.
“And then the one hits the post - the boy shoots and it hits the inside of the post and it comes out when you're saying: ‘This is going in’. So moments like that didn't quite go our way.
“But we came, we gave them a good go, it was just not good enough.”
Moyes added: “I'm beginning to see the players do well in lots of the big games, but we've got to find that way of being clean when we finish or just getting the little bit that makes a difference.
“We've won quite a lot of games away from home. There was a period where I was saying: ‘Oh, this could be Everton again here, somewhere late in this game this could happen, but it just went the other way.”