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Wets Ham needed goalkeeper Joe Hart to keep them in the competition after his saves from Mat Sadler and Shaun Whalley secured a 0-0 third-round draw at Greenhous Meadow.
The League One hosts were the better side throughout even though Moyes made just four changes from Thursday's 1-1 Premier League draw at Tottenham.
And Moyes was upset with the Hammers' commitment.
"I don't think we showed any quality and the biggest disappointment is I didn't think we showed enough steel," the Scot said.
"When you come to places like this you have to show yourself physically, that you can battle and compete.
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“The biggest disappointment is I didn't think we showed enough steel”
David Moyes
"I didn't think we did that at all and that was the worst thing about it. Sometimes it's not easy.
“The conditions - the sun - didn't make it easy for the players to see things around them but that didn't stop the fact that we didn't compete on a lot of occasions.
"Obviously if you compare Wembley and Thursday night, it's a big change. But it's a mentality thing.
“You've got to go and show that wherever you are, you've got to respect whatever players you're against and recognise it's going to be tough.
“For the first half especially, we didn't compete at all."