Strikes from Danny Ings and Mohamed Salah seemingly put Liverpool in control of the game.
But two late goals from Jake Livermore and Salomon Rondon saw West Brom claim a point.
The draw sees Jurgen Klopps side remain third, however, they missed the opportunity to open up a five-point cushion on fourth-placed Tottenham, while Chelsea are now eight points off Liverpool with a game in hand.
The game also saw Albions Ahmed Hegazi live a charmed life as the defender appeared to punch Ings in the stomach after a 50-50 challenge between the two, but referee Stuart Atwell did not see the incident.
Ings could have also won a penalty for his side in the second-half after Craig Dawson tripped him up but Atwell was not interested.
And Klopp felt Liverpool were on the wrong end of the crucial decisions.
Speaking to talkSPORT's Adam Bridge after the game, Klopp said: "It was a difficult game. We controlled it but the pitch was quite dry and it was difficult to play football. But the boys adapted to it and played really well in the first-half.
"With set pieces they were always going to be a threat and I thought we dealt with that really well until the last 15 minutes.
"Their first goal was similar to our first one and the second one was not a free-kick. It wasnt a foul so that was unlucky for us.
"I think we all agree it could have been a penalty on Danny [Ings] and Hegazi could have finished the game a little bit earlier."
Klopp named a slightly weaker side than usual as Liverpool have the first leg of their Champions League semi-final tie with Roma on Tuesday night.
And the team seemed to struggle with the intensity of the game in its closing stages, which saw the likes of Alberto Moreno, Ragnar Klavan and Joe Gomez appear out of their depth on occasions.
But the German jumped to the defence of his players.
Klopp added: “Alberto [Moreno] has not played for a long time and was injured two weeks ago, Joe [Gomez] has come back from injury.
“Ingsy [Danny Ings] has not played a lot and Ragnar [Klavan] has not played a lot and was injured so its clear that it was always going to be a bit difficult for the boys.”