Video assisted refereeing (VAR) came to Liverpool's assistance twice in the first half but even that wasn't enough to help the reds who were knocked out of the FA Cup.
The reds started the game with an early goal before going on to lose against the Premier League's second from bottom side, just days after losing away at Swansea who are at the base of the table.
When Firmino lobbed the keeper in the 6th minute there was no indication of the eventual disappointing outcome at Anfield.
Within a minute Jay Rodriguez had levelled for West Brom after Gareth Barry snapped the ball away from Gini Wijnaldum before Brunt passed the ball for Rodriguez to fire past Mignolet.
Simon Mignolet was brought back to the side in order to keep him fresh, alluded Klopp before the game. He was certainly kept busy on the night picking the ball out of his own net.
With just 11 minutes on the clock, West Brom had a 2-1 lead.
Gibbs sent the ball through the reds defence and Rodriguez scored his second.
From a corner Dawson headed past Mignolet again, but VAR was called on to signify that Gareth Barry had been standing in front of Mignolet so the score remained 2-1.
Then at the other end Mo Salah was dragged down in the area by Jake Livermore, after an age and after consulting with the pitchside monitor, the referee Craig Pawson signalled the penalty.
But Firmino could only smash the penalty onto the crossbar. And this would be a heavy price for Liverpool as deep into injury time West Brom made it 3.
Krychowiak sending over the ball that caused panic and allowed Matip to put it into his own net.
There was little signs of a fightback from Liverpool - Mo Salah did give the reds some hope when he scored in the 78th minute but it was a poor performance from the reds and caps a horrible week of two defeats, and the first Anfield defeat since last April.
Next up for the reds is a trip to Huddersfield in the Premier League.