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The Brazilian was at fault for Wolves' first goal, gifiting Goncalo Guedes an easy finish with a mis-directed pass, while he then conceded a soft second to Hwang Hee-chan.
Darwin Nunez and Mohamed Salah both struck to ensure the holder did not suffer a shock third-round exit at Anfield, with a replay to come at Molineux.
Speaking afterwards however, Klopp did not lay his side's problems at the feet of his goalkeeper, instead praising what Wolves brought to the table in an engaging contest throughout at Anfield.
"The goal should not happen but we all know how often Ali saves our backsides," he told ITV Sport.
"They had counter-attacks before then [too].
"It is always dangerous when [Adama] Traore gets the ball, we could see that.
"We came back with a fantastic equaliser. They got a foot in the game, and they caused us massive problems."
Liverpool came closest to an exit when Toti Gomes had a finish controversially ruled out by the linesman's flag, with VAR unable to offer enough angles to confirm whether the player was onside.
The decision sparked a furious reaction from Julen Lopetegui, and Klopp acknowledged it was not an ideal situation for both teams.
"I'm not sure about their third goal," he said.
"We have one picture where it may look offside.
"I can understand why they are angry about it. We don't want the VAR to just have one angle."
Lopetegui was left infuriated by the decision that robbed his side.
"We have seen it and the offside doesn't exist," he told ITV.
"It's impossible but someone has told him that it is offside. We have seen the image and it doesn't exist.
"The decision is wrong. I make mistakes every day and sometimes they do too.
"Today we have the help of VAR, and it is a pity, because I'm sorry, it's not offside."
Meanwhile, Cody Gakpo enjoyed a solid debut for Liverpool after his arrival from PSV, and Klopp was warm in his praise for the Dutchman.
"He fitted into the game," he said.
"It was not easy for a first step. We cannot expect it to be perfect.
"He showed good signs. We have to get him in better positions, but that will come, no doubt."