Brendan Rodgers possesses a forward line that is envied across Europe, but there remain lingering doubts over his defence, highlighted here by an appalling error from Kolo Toure.
The sight of Toure holding his head in hands in despair after Victor Anichebe's equaliser will prove one of the enduring images of Liverpool's season if they fail to end their five-year Champions League exile.
Toure's mistake was inexplicable, producing an inch-perfect pass across the face of his own goal to Anichebe, and it was a moment that could prove significant in the Merseyside battle for a top-four place.
This was a huge chance wasted after their demolition of Everton on Tuesday, the gap between the clubs now two points.
For all the frustration Liverpool experienced in the transfer window, failing to recruit either Mohamed Salah or Yevhen Konoplyanka despite lengthy pursuits, it may be remiss of Rodgers to have not addressed the position that has been problematic for most of the season.
They have now only managed to keep one clean sheet in 11 away games, a worrying statistic.
After dominating the first half, taking a deserved lead through Daniel Sturridge, Liverpool were relatively untroubled until Toure's rush of blood to the head enabled Anichebe to earn West Brom a point.
Anichebe's five months since leaving Everton have barely merited a mention but his mobile phone is likely to have been bombarded with text messages from his old team-mates after the game.
Though Rodgers insisted the point was a positive one, this was undoubtedly another frustrating visit to the Black Country for the Liverpool manager.
In August 2012 he was given stark notice of the rebuilding job ahead as his new team suffered a chastening 3-0 defeat in his first game in charge and while this was never as uncomfortable, it was a missed opportunity to strengthen their hold on the final Champions League place.
It seems that Rodgers's fingernails are in for a torrid time over the final weeks of the season.
While Toure's howler increased fears over where their mission may be threatened, the goalscoring form of Luis Suarez, who made his Liverpool debut three years ago to the day, and Sturridge continues to prove remarkable.
They had already scored 39 goals between them before this game and combined for the 40th after 24 minutes.
It required a typical flash of invention to puncture the early tedium, with Suarez crossing from the right to present Sturridge with the simplest of finishes from almost on the goalline.
Friends reunited, after their unseemly spat at Anfield just last week.
Liverpool should have added a second goal when Albion's defence failed to adequately clear Philippe Coutinho's corner but Toure's shot was tame and Ben Foster saved easily.
Albion's defending at Aston Villa on Wednesday night will have given new head coach Pepe Mel sleepless nights and the first half was at times embarrassingly one-sided, with the departure of Jonas Olsson with a hamstring injury only adding to the concerns.
Then Diego Lugano, so woeful at Villa Park, was introduced as his replacement to collective groans from the home supporters.
There was a brief respite when Zoltan Gera almost found the corner from 20 yards but Albion lacked fluidity and appeared confused by the new pressing approach imposed by Mel.
Whatever Mel said at half-time earned a response, however, for the second half was a vast improvement on the first.
Chris Brunt sent a free-kick over the crossbar before Simon Mignolet produced an excellent save from Gareth McAuley's powerful header.
Liverpool sorely needed a second goal.
It nearly came from Suarez, as he escaped both McAuley and Lugano too easily with a simply executed flick but his shot was brilliantly repelled by Foster, in front of a watching Roy Hodgson.
It proved costly. Anichebe had only been on the field for three minutes, earning predictable abuse from the travelling fans.
But after Toure was given the ball by Mignolet and then delivered a pass across the penalty area without an Albion player near him, Anichebe took one touch before driving the ball into the bottom corner.
Suarez's frustration increased, with a needless foul on Claudio Yacob on the halfway line earning a deserved booking.
Foster came rushing out of his goal to deny Sturridge as time ebbed away but it was Albion who finished the stronger team.
Mel remains only one point above the dreaded dotted line but there have been tangible signs of progress since his arrival.
For Rodgers (left), the visit of Arsenal next weekend will represent yet another litmus test of Liverpool's credentials. (© Daily Telegraph, London)