The visitors looked to be heading for a comfortable win thanks to goals from Danny Ings and Mohamed Salah, only for Jake Livermore and Salomon Rondon to score in the final 11 minutes and snatch a 2-2 draw.
Klopp was angry at the award of a free-kick against Joe Gomez that led to Rondon's equaliser, while he also criticised referee Stuart Atwell for failing to award a penalty for a Craig Dawson challenge on Ings and a blatant punch by Ahmed Hegazi on the striker.
He also accused West Brom of deliberately not watering the pitch in order to hamper Liverpool's passing game and suggested it is a tactic they are preparing to use next season, when they will likely be in the Championship.
“What is the story now?! West Brom’s useless comeback," Klopp joked to reporters when it was suggested that Ings' goal was overshadowed by Liverpool throwing away the lead.
"I think we controlled it pretty well. It was clear they would pretty much only have opportunities with set-pieces; the rest we defended really well," the Liverpool manager added to Sky Sports.
"We scored the second and then gave them the corner. It's difficult. The whole game, the block on the goalkeeper, I know everyone likes it in the country but it makes life difficult for the goalkeeper in these situations. The second, what my guys told me, it was not a foul.
"It was a difficult game, especially after the pitch got drier and drier, we had the ball constantly and it's not so easy. West Brom obviously decided not to water the pitch at half-time again. It was quite difficult.
"We had the situation early in the second half, Ings in the box, that could be a penalty, and Hegazi and Ingsy... I don't know, you need a little bit of not even help, only the right decisions."
When asked to explain his frustrations with the surface, he replied: "I was not happy with the pitch. You never played football, obviously. It makes a massive difference. If you're like West Brom, the ball constantly in the air, you don't need a wet pitch.
"That's how it is and we have to deal with that. They can do it next year, playing with a dry pitch in the Championship."
He added on Hegazi, who is likely to face retrospective punishment for the Ings incident: "I don't have to say anything about that. I don't know why he did it, but he did it.
"With the penalty situation, people are laughing at Ingsy that he goes down. Nobody can stay on their feet in that situation.
"We know what we are responsible for but, with the number of games, stuff like that, you need only the right decisions. Then it's fine at the end because we win here 3-0, 3-1.
"Everyone knows they want set-pieces in the last few minutes and the ref gave it to them, in the corner with Joe Gomez. Everybody told me it was not a foul."
Klopp could not even bring himself to publicly congratulate Ings on his first Premier League goal since October 2015.
Asked how happy he was with the striker's finish, he replied: "Very. He could have scored a second. I'm not in a mood to talk about positive things. Give me a night to sleep on it and I'll tell Danny how happy I am."