Boss Sam Allardyce has this week brushed off criticism of his side's style of play, claiming teams that gain promotion need to know how to win ugly.
But a stalemate at home to the side who kicked off propping up the division will be hard to stomach for the second-placed Hammers.
In fairness they would surely have won at a canter had Frederic Piquionne's radar not deserted him in front of goal, while Kevin Nolan was twice denied by David James and Freddie Sears was a whisker away when he rattled a post.
But City, full of confidence after a first win under new boss Derek McInnes on Saturday, were themselves a threat on the break and also hit the woodwork.
Allardyce was forced into an early reshuffle when Winston Reid suffered a nasty shoulder injury defending a City corner in the seventh minute and had to be replaced by Abdoulaye Faye.
Nevertheless, the hosts almost opened the scoring after a quarter of an hour when young striker Sears curled his shot from outside the area onto the foot of the post.
Unfortunately, it was to be the closest they came all game.
Former Hammers keeper James kept out Piquionne's downward header with an extravagant diving save and also stuck out a hand to divert Nolan's low shot, but West Ham did not have everything their own way in the first half.
Robert Green was fortunate to see Marvin Elliott's shot deflected straight at him and was even more relieved when Neil Kilkenny's daisy-cutter wrong-footed the home defence but clipped the side of the post.
West Ham should have taken the lead on the stroke of half-time when Julien Faubert's cross was met by Piquionne but the French striker's header was too close to James.
Moments after the restart Piquionne fired another good opportunity into the side-netting and then headed straight at James again.
None of skipper Nolan's four goals this season have come at Upton Park but he must have thought he was about to break his home duck when put through by Piquionne, only for James to spread himself well and save with his legs.
Still the chances came and went, with Faubert blazing over the top and substitute Carlton Cole following suit.
But the winner just would not come - and it could have been a whole lot worse for Allardyce but City sub Yannick Bolasie fired narrowly wide in the 89th minute and Green had to finger-tip a deflected corner wide in stoppage time.
Nonetheless, City celebrated a hard-earned point to leave Allardyce and an increasingly disgruntled home faithful frustrated.