Moyes' side will be thankful for Joe Hart after the England global goalkeeper continued to deny his former boyhood club, however, supporters took to Twitter to lament the performance of one of their other players.
Joe Hart kept West Ham in the FA Cup after the Hammers survived a scare at his old club Shrewsbury. After Cheikh Kouyate failed to get a telling touch to a risky cross by Cullen in the ninth minute, any whiff of a first-half breakthrough by the away team vanished.
The Hammers needed Joe Hart to keep them in the competition after his saves from Mat Sadler and Shaun Whalley secured a 0-0 third-round draw in Shropshire. I would have took a hat, sunglasses all sorts, I couldn't see a thing.
Declan Rice in Hammers action
"I was a substitute against BATE Borisov in a Europa League game and I was called to get stripped to come on - but I didn't have any shinnies". Nevertheless, the 30-year-old insisted the Sky Bet League One sides' performance didn't come as a surprise to the East Londoners: "No, no, I don't think so, he said after the match".
Hart earned praise from boss David Moyes after being recalled following four games on the bench, while the England worldwide has not played in the Premier League since November. "But Shrewsbury had their own problems coming into the game that they had to deal with as well". "Shrewsbury were better than us today so I'm pleased to still be in the FA Cup", said Moyes. We were up on them and rattling them the whole game. However, he remained positive, explaining: "You can't live in fear, you've just got to play and enjoy it".
"I should be surprised but I wasn't. Anything is possible when it is 11v11, so we will go there and have a right go at them".
Most of Moyes's troops did not look like they relished this duel. "Maybe a few of the boys were exhausted, we have had a lot of games recently".