"I don't think we showed any quality and the biggest disappointment is I didn't think we showed enough steel", he said.
The League One high-fliers had the better of the contest and West Ham's former Shrews goalkeeper Joe Hart had to be alert to save Mat Sadler's close-ranger shot and Alex Rodman's powerful drive in the first half.
Moyes made only four changes to his side for the cup tie, which will be replayed at the Olympic Stadium during the week beginning January 15.
"When you come to places like this you have to show yourself physically, that you can battle and compete".
Rusia exige a Trump abstenerse de interferir en asuntos internos de Irán
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Moyes knew his side had escaped from a game where they created very little in the way of chances of their own, adding: "I don't think we hardly had any attempts at all, one or two maybe but very few". Sometimes it's not easy.
"Obviously if you compare Wembley and Thursday night, it's a big change.
Shrewsbury were better than us today so I'm pleased to still be in the FA Cup", said Moyes. 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. "In the first half we were never at it, we were never at it in the game really but particularly in the first half", Moyes told BBC Sport.
"There are not many Premier League teams that win games easily in the cup at this stage, they are hard games to win".