The Toffees were blown away by three goals in three first-half minutes at home to Wigan and offered little in the way of a fightback to exit the competition with a whimper.
"Wigan played well and on the day we didn't play well," Moyes said. "We've not had many of those days this season, probably not had many of those days since January last year.
"This was one of those days where it didn't go well at all and we just didn't perform.
"We were fortunate as they had hit the post (before the goals) but there were one or two signs we were getting organised to deal with it but we were soon a couple of goals down.
"I thought we tried everything we could at the start of the second half, but on the day we didn't make the goalkeeper work hard enough,
"We can't argue, Wigan were the better team on the day. We can't complain, we weren't good enough.
"We never really got to grips with the game. We just didn't look as if we had the creativity which would make that happen.
"When you lose one goal you're saying, 'Calm down, it's not the end of the earth', but unfortunately we conceded by giving a really poor second goal away."