The Hammers went down 2-1 away from home, squandering their chances of reaching the Carabao Cup semi-finals.
"The players showed great determination and character," Moyes said after the game.
"They put in a brilliant effort. In my mind, there was a couple of really poor bits of defending which gave them the opportunity to score. It was self-inflicted.
"We were unfortunate that a couple of big chances didn't go in. It was a tough game and we let ourselves down on a couple of incidents in the first half, but overall the players did a great job."
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