A first-hald strike from Matthew Mills secured the tie for the Championship outfit but Everton had their claims for a penalty turned down in the second half by Andre Marriner when Reading defender Ian Harte appeared to handle the ball in the area.
Moyes told ESPN after the game: “I’ve seen it there I think it was a penalty, it hits his arm. It would be unfortunate but it did hit his arm.”
The Royals got the only goal of the game after 26 minutes when Matthew Mills volleyed in from a corner which Everton failed to clear.
Moyes believes it was frustrating to get knocked out in this fashion at home especially after defeating holders Chelsea at Stamford Bridge in the last round.
“It was really disappointing for us, because we done so well in the round previous and we were setting ourselves up to try and get through and as I said in my programme notes you can only ever ask for a home tie and we didn't take advantage of it.”
The Toffees boss was full of praise for the Championship side and thought as soon as they got the goal it was always going to be difficult for his team.
"They were terrific the way they went around their job, the two forwards keep you occupied all the time. I actually thought we coped; they had one or two chances, mainly from our mistakes or from us trying to win the game.
“I thought in the early part of the game we controlled it but when you give away the goal it gave them something to defend and we had to start chasing it and the longer it went on then obviously the more we became.”
Moyes was critical of his side’s effort going forward and believed they didn’t create enough chances to get back into the tie.
The Scot brought on Victor Anichebe and Jermaine Beckford on at half-time but he was disappointed with their performances as they did little to change the outcome of the game.
“I thought we had one or two things but not enough. They defended very well. (Coleman’s header)That was a big chance for us at the back post with a header.
“They got back behind the ball and we just didn’t have enough craft in the final third of the pitch to make anything happen.
Asked if bringing on Beckford and Anichebe had the desired effect Moyes said: “Probably not tonight, no, but we weren’t having the desired effect so we had to try something.”
The Everton manager is targeting the Toffees next fixture away at Newcastle as a chance to respond to the result and says it is important that his team turns up.
“We’ve got a game on Saturday, so we have to be there, we have to play we have to try and do everything we can to get the points.”