Albion were unable to make it four wins on the bounce after Nottingham Forest scored in the last minute to earn a point.
The Baggies looked to be on course for a deserved victory after a stylish display saw Callum Robinson get off the mark for Albion an own goal from Forest defender Tobias Figueiredo.
But with the game deep into injury time, Forest defender Matty Cash fired an unstoppable effort past the diving Sam Johnstone to keep their play-off hopes alive.
"I told the guys I'm going to be disappointed and they're frustrated, but if we continue like this, with the same patterns, focus, energy and quality, then we really have a good chance to do what we want to do," said Baggies boss Slaven Bilic.
"This was our best performance, whatever the result - we were always the ones who were better, in ball possession, in number of great situations, creating chances, everything was there.
"The only thing that was missing was to kill the game at 2-1. But some of our finishing was not good enough, and the goalkeeper made a few good saves."