Manager Jurgen Klopp said Liverpool only had themselves to blame after West Brom snatched a shock 1-1 draw at Anfield.
The Baggies remain second bottom of the table, but gave their chances of survival a huge boost by becoming the first side to take points off Liverpool at home this season in Sam Allardyce's second match in charge.
The Premier League champions seemed set for a comfortable 90 minutes as Sadio Mane's fine finish gave them a 12th minute lead.
Liverpool's dominance of possession reached 84 per cent in the first-half as West Brom struggled just to get out of their half.
However, the visitors grew into the game in the second-half and got their reward when Semi Ajayi headed home from a corner.
"It was our own fault," said Klopp. "We gave them simple corners and that's the only thing they wanted to have tonight.
"To be fair West Brom did their job inside 90 minutes. They deserved the point tonight because we didn't finish the game."
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