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Avran Grant's side are below second bottom Wolves on goal difference as their wait continues for a first league win since September 25.
The draw was some kind of vindication for Blackpool boss Ian Holloway, who had threatened to quit if fined by the Premier League for making 10 alterations for the midweek defeat at Aston Villa.
Holloway made 11 changes here as he recalled all his regulars and they responded with a solid display that kept the Seasiders outside the relegation zone.
However, it was referee Kevin Friend who took centre stage when he denied the home side what looked two clear first-half penalties, with Grant's men then unable to make the most of their opportunities as the Israeli again faced calls for his resignation at the final whistle.
West Ham had what looked a strong penalty claim turned down by Friend when left-back Stephen Crainey appeared to trip Pablo Barrera out on the right touchline.
The home side were again screaming for a spot-kick when Victor Obinna's fierce 18-yard drive struck Craig Cathcart on the arm, but once more the referee was not interested.
Blackpool had to replace goalkeeper Matthew Gilks at the start of the second half, after he had appeared to jar his knee when clearing a goalkick, with Richard Kingson coming on for an unexpected second appearance of the week.
West Ham had another great chance when Luis Boa Morte was slipped into the left side of the penalty area by Scott Parker, but dragged his shot wide of the far post.
Blackpool captain Charlie Adam spotted Robert Green off his line and so tried an audacious chip from just inside the West Ham half which, fortunately for the backpedalling keeper, dropped over the bar.
Blackpool substitute Marlon Harewood almost returned to haunt his former club, but his scrambled goal from a free-kick was ruled out for offside.
West Ham substitute Carlton Cole almost had an instant impact but his deflected close-range effort struck the outside of the post.
There was a let-off for the hosts when Harewood somehow stabbed the ball wide from six yards before Green deflected away a goalbound effort from Cathcart.
In stoppage time, Benni McCarthy headed over as the Hammers were booed off by their increasingly depressed supporters.