Klopp’s side took a two-goal lead thanks to strikes from Danny Ings and Mohamed Salah, but they were rocked by Albion’s dramatic fightback.
Jake Livermore got one back with 11 minutes left before Salomon Rondon equalised in the 88th minute.
It was a frustrating warm-up for next week’s Champions League semi-final first leg against Roma and seemed to put Klopp in a bad mood.
The Reds boss expressed disappointment with Albion’s decision not to water their pitch, bemoaned referee Stuart Atwell’s refusal to send off Ahmed Hegazi for appearing to punch Ings and claimed Liverpool should have had a penalty.
“It was a difficult game as the pitch got drier and drier. West Brom decided not to water the pitch at half-time and that makes it difficult,” Klopp groaned.
“It makes a massive difference. A team like West Brom do not need a wet pitch, they can do it next year playing on a dry pitch in the Championship.”
Asked about Hegazi’s clash with Ings, Klopp added: “The analyst showed it to me, I don’t have to say anything about that, I don’t know why he did it, there is no reason.”
On Ings’ penalty appeal, Klopp said: “People laugh at Ings when he goes down, but I don’t know anyone who doesn’t go down in that situation.
“We need the right decisions, everything would be fine and we win 3-0 or 3-1.”