The Black Cats won 2-1 on penalties after a dramatic conclusion to extra-time to progress to Wembley, where they will face Manchester City on 2 March.
“I am disappointed. We didn’t play well enough over the piece,” said Moyes.
“If we were going to do it we were going to stumble over the line.”
“I didn’t think we played well enough on the night. We had opportunities to score a second goal and put ourselves in a better position but we didn’t do it.
“It is disappointing but it is part of the job. There has always got to be a loser in a semi-final and it happened to be us.
“I think there have been other games where we have played well enough and not won but I didn’t think we played well enough here. The goal was a bit unlucky for David De Gea but, again, we didn’t play well enough.
“I didn’t think we tried to hang on to anything when we were ahead. I don’t think we could have put more attacking players on if we had tried. We had opportunities to finish the game off but we didn’t take them.”