Goals from Aidan White and Rudolph Austin put the hosts into a great position, before Sylvain Distin pulled one back for the Toffees close to the end.
David Moyes admitted his frustration after being knocked out of the competition, and berated a poor first 45 minutes after the loss.
“We were not very good in the first half, but we got better in the second, but not as good as we’ve been playing,” The Daily Mail quote the Scot as saying.
“We started terribly, gave them the initiative and lost the game in the opening 20 minutes due to the way we started.
“We gave away a really poor first goal and left ourselves trying to get back into the game.
“These boys are in the squad and have to be able to show they can come in and play. If you don’t use them, what’s the point in having them? The players want to play and be involved,” he concluded.
By Gareth McKnight