The home team came close after a quarter of an hour when Freddie Sears' curling, long-range strike hit a post.
But Neil Kilkenny almost scored for the away team when his low shot also clipped a post.
In the second half, City keeper David James twice kept out Frederic Piquionne headers and was also alert to stop a strike from captain Kevin Nolan.
West Ham manager Sam Allardyce has spent the week brushing off criticism of his side's style of play, claiming teams that gain promotion need to know how to win ugly.
But the Hammers were unable to do that on this occasion and this stalemate, against a side who were bottom at kick-off, left the home fans further frustrated.