"If we'd gone through I'd have been disappointed in the performance, but obviously I'm doubly disappointed because we didn't get through. With a minute to go, we were in the final.
"We didn't play well enough tonight and Sunderland came here and deservedly got themselves into the final."
Bardsley’s shot for Sunderland's goal on the night squirmed past David De Gea, but Moyes preferred to focus on the Reds' failings from the spot.
Danny Welbeck, Adnan Januzaj, Phil Jones and Rafael all missed, leaving captain Darren Fletcher as the only Red who was successful with his penalty.
"David has been very good this season but the players got us out of the hole at the time," Moyes said. "I know it didn't get us through but it at least gave us a chance when it went to penalties. We were terrible at penalty kicks, terrible.
"Maybe on another day we'd have had a different set of penalty takers. But that's what we had available to us on the night. It just didn't quite work.
"I think the bigger disappointment was how we played in the game."