After the scoreline being level at 3-3 after extra-time at Old Trafford, both sides took turn at missing spot kicks before the Black Cats eventually won the shoot-out 2-1.
And Moyes was understandably disappointed with the way in which his side wasted a number of chances to progress to the Final, particularly the poor standard of penalty taking in the shoot-out.
“With an minute to go in extra time we were just about there and we had opportunities to score a second but didn’t do so,” Moyes told MailOnline.
“We went to penalties and our penalties were terrible. There is always going to be a loser in Semi-Finals and it happens to be us.
“We went in with fresh players to give us energy. We had chances to finish it off and didn’t. We had to defend a few corners but I repeat, we didn’t play well enough.”
And Moyes also confessed his unhappiness with goalkeeper David de Gea’s howler that let Sunderland back in the game late in extra time, as well as his side’s penalty takers.
“Keepers do make mistakes, but it was a costly one,” he added.
“That was really poor [the penalties], but that happens in football.”