The Hammers struggled to create anything of note across the 90 minutes of the FA Cup third-round tie and were arguably the happier of the two teams to see the game end all square.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Hart; Burke, Rice, Reid, Ogbonna, Masuaku; Kouyate, Obiang, Cullen; Ayew, Hernandez
SUBS: Adrian, Neufville, Makasi, Quina, Haksabanovic, Samuelsen, Martinez
STARTING XI: Henderson; Godfrey, Sadler, Beckles, Whalley; Ogogo, Morris, Bolton, Nolan; Nsiala, Rodman
SUBS: MacGillivray, Lowe, Dodds, Gnahoua, John-Lewis, B. Morris, Payne
Paul Hurst: "We aren't all going to go home and think that's the end of the road and our season's over if we lose against West Ham, so I want us to try and be as positive as possible, but with it in mind that we are playing against higher quality."
David Moyes: "Do I want to win the FA Cup? 100%. But I don't think it can be where we can damage our league season. If I could win the cup I would definitely try to win the cup, but I couldn't do it if I thought it would affect the Premier League."
SHREWSBURY TOWN SUBS: MacGillivray, Lowe, Dodds, Gnahoua, John-Lewis, B.Morris, Payne
WEST HAM UNITED SUBS: Adrian, Neufville, Makasi, Quina, Haksabanovic, Samuelsen, Martinez