The Reds dominated the match for long periods, but they were unable to find a way through the well-organised hosts and the draw left them six points behind fourth-placed Manchester City.
After an uneventful first half, West Brom goalkeeper Boaz Myhill pulled off a superb double save to deny Philippe Coutinho and Jordan Henderson.
Jordan Ibe also hit a deflected effort onto the top of the bar, while substitute Callum McManaman went closest for West Brom with a low shot which was blocked by Simon Mignolet.
Liverpool made a lively start, with Raheem Sterling and Ibe threatening on the flanks as the Reds showed no sign of a Wembley hangover following their FA Cup defeat to Aston Villa.
But despite dominating possession, the visitors struggled to create clear-cut chances. Coutinho failed to hit the target from 25 yards and Steven Gerrard, making his 500th Premier League appearance, curled a free kick narrowly over after Mario Balotelli was fouled on the edge of the box.
Coutinho was at the heart of the action, and the Brazilian tried to catch Boaz Myhill out with an audacious effort from the halfway line. The West Brom goalkeeper was off his line but Coutinho???s shot trickled harmlessly wide.
Balotelli was next to try his luck when he lashed a first-time effort narrowly over from the left-hand side of the box, but the Reds came no closer to breaking the deadlock before half-time. West Brom, meanwhile, were well-drilled at the back but offered next to nothing going forward in a one-sided first period.
Liverpool continued to dominate after the break and they were desperately close to scoring in the 55th minute. After Balotelli???s effort was blocked, Myhill got down low to save Coutinho???s follow-up before somehow blocking the rebound from Jordan Henderson at point-blank range.
It was a lucky escape for the Baggies, but they almost broke the deadlock against the run of play moments later when Craig Gardner volleyed Chris Brunt???s deep cross into the side netting.
The game had come to life, and Ibe was inches from putting the Reds in front when he played a one-two with Balotelli before firing a deflected effort onto the crossbar.
Once again, West Brom responded by carving out a chance of their own. Martin Skrtel failed to clear a cross from the right and James Morrison sent a looping header beyond Simon Mignolet, only for Dejan Lovren to make a crucial goal line clearance. ??
Liverpool piled on the pressure at the other end as Lovren scooped a corner over the bar and Gerrard shot straight at Myhill, but still they struggled to find a way through the blue and white shirts.
West Brom substitute Callum McManaman sent a shot straight at Mignolet on a rare foray forward from the home side, before Coutinho attempted another long-range effort at the other end. Myhill looked beaten but his dipping drive landed on the roof of the net.
Brendan Rodgers sent on Fabio Borini and Adam Lallana in the closing stages, but neither was able to make the difference.
In fact, it was West Brom sub McManaman who came closest to breaking the deadlock when Mignolet saved his diagonal shot with his legs after ghosting past Skrtel.
Lovren headed a Gerrard cross over the bar at the death, but there was to be no late winner for the either side.??