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Mohamed Salah put Liverpool ahead and Joel Matip doubled the visitors’ lead before half-time at the London Stadium.
Manuel Lanzini reduced the deficit, but woeful West Ham capitulated and Alex Oxlade-Chamberlain netted Liverpool’s third before Salah bagged his 12th goal of the season to seal the rout.
A disappointed Bilic said his side had started well but then conceded two “cheap” goals.
“We tried to change the shape and be more open in the second half, we scored but they are so good on the counter attack,” he said. “It is a big defeat for us.
“It’s not a lack of effort. We should have defended better. It’s no excuse to concede from your own corner kick. At this level if you are 2-0 down so early it’s not game over but it’s very difficult to come back.
“I have to talk to the chairman, we are going to discuss this defeat. It’s not the first one, it’s the second in a row in home. It is a very difficult situation for me.”
When asked if he still had the club’s backing he said: “It’s hard for me to talk about that now.”
But Liverpool manager Jurgen Klopp was delighted with his team’s showing.
“The result, it feels good,” he said. “We changed our approach, it was a counter-attacking line-up to use our speed from a deep situation.
“It was brilliant play for the first goal.
“Our counter-attacking was pretty perfect, we had some wonderful play. Roberto Firmino, I’m not sure I’ve ever seen a player play a third game in the week with such intensity and I’m a few days in this business.”
“It’s a really good week,” he added. “It’s a good moment to have a little break. We lost our skipper overnight and Gini Wijnaldum did not have his boots here. We thought he had no chance of playing, we only brought him here so he is nearer to Amsterdam, he was flying there to see the doctor.”
The victory took Liverpool back to sixth position in the Premier League table but West Ham, with just two league wins all season, are just one point off the relegation places.
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