The Reds fell to a surprise 3-2 defeat to David Moyes' side as they fell below their opponents to fourth in the table.
West Ham took the lead when Pablo Fornals' corner was punched into his own net by Alisson.
However, Liverpool were unhappy because they felt the Brazilian had been fouled.
A few minutes later, they were calling for a red card as Aaron Cresswell lunged in on Jordan Henderson. But VAR decided not to intervene.
Trent Alexander-Arnold did equalise in the first half for Liverpool but second half strikes from Fornals and Kurt Zouma put the home side 3-1 ahead.
Divock Origi pulled a goal back but it was too little, too late for Liverpool.
After the match, Klopp left everyone know what he thought of a few decisions during the match...
VIDEO: Jurgen Klopp's interview after West Ham defeat
"The first goal is a foul on the goalie," he told Sky Sports. "The arm goes against Alisson's arm so how can he catch the ball when someone pulls his arm away. It makes no sense. It's the typical excuse that VAR says it's not clear and obvious but then what do you need?
"What can [Alisson] do? That's why the goalie is protected in moments. If a player goes up with his arm for a goalie that's an important position of the body and if that's in the way how can he make a save?
VIDEO: Alisson's own goal
"People will say I'm looking for excuses, I'm not. I accept we're not too good to lose football games. Today we lost it, that's not nice but I accept it. But when we speak about situations in a game you just need normal decisions from a referee. He didn't do that.
"Cresswell? For me it's a reckless challenge. Even though he touches the ball, you can't go in like that as anything can happen. You can say he touched the ball but you have to control your body.
VIDEO: Cresswell's tackle on Henderson
"Those two situations were influential in the game but in the end West Ham fought for the three points. They are not responsible for the decisions the VAR made."
He later added: "It's a clear foul on Alisson, how can it not be? The arm from Ogbonna is there. I don't know who is VAR today.
"The ref made it easy for himself, and said let's see what the VAR said, they said it's not clear and obvious. It was really strange."
On the Cresswell challenge, Klopp added: "The way I saw it it's a clear red card. There's actually no discussion possible. They will say because he touched the ball, but a reckless challenge you can touch whatever you want before. If you hit your opponent high up the leg, on the chin, you cannot go like this in a challenge. That's it. But we cannot make these decisions."
Klopp also had time to moan about West Ham's performance by saying it was the 'old West Ham.'News Now - Sport News