After winning the semi-final second leg at Old Trafford after extra time and levelling the tie at 3-3, United missed four of their five spot-kicks in the penalty shootout to crash out of the tournament.
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"If we were going to get through, we were going to stumble over the line, not because we played well enough," Moyes told reporters.
"We didn't play well enough to merit going through - Sunderland came here and deservedly got themselves in the final.
"In the end, I just don't think we got the level of performance we needed to get through the game. It went to penalties - and our penalties were terrible.
"But the bigger disappointment was how we played. Of course you would expect a better standard because, don't forget, there were a lot of internationals out there.
"It's part and parcel of the job at times. There's always going to be a loser in a semi-final and it happens to be us. We didn't execute our penalties well enough."