Virgil van Dijk managed to find a 100th minute winner for Liverpool as they won 2-1 at Hill Dickinson stadium on Sunday.
Asked if Everton can be pleased with their performance on the day, Moyes said: “Yeah, but it doesn't make me feel any better, that's for sure.”
He continued: “The players have been told that I thought they'd done a great job today in the main.
“There were periods in the game where Liverpool had a bit of control. But there were long periods in the game when we had control as well.
“We had big opportunities, especially in the first 20 minutes or so. I didn't think we offered Liverpool too many chances in the whole game, to be honest.
“It didn't feel as if we'd given up too many opportunities, so the players have done a good job, but had no rewards out of today.”