The Reds, fielding nine changes, failed to recover from a poor first half that saw the Sky Bet Championship side go 2-0 up thanks to goals from Richard Stearman and Andreas Weimann.
Divock Origi set up a nervy final five minutes with a close-range effort but it was not enough as Liverpool suffered their third home defeat in a week for the first time since 1998 to leave their season in tatters.
“A very bad performance,” Klopp told BT Sport. “It started bad and didn’t get really better.
“There is not a lot of good things to say about this game. It is difficult, difficult to explain.
“The start gave them immediate confidence. We were not ready. We had the ball, gave it away and made a foul.
“We tried but it was not good enough in the first half. Second half was better, it should be better, but not a lot more to say.
“I’m responsible for it. You learn a lot about players in situations like this. I am responsible for this performance, 100 percent.”
Stearman headed Wolves ahead inside the first minute and Weimann, on loan from Derby, knocked the wind out of Liverpool’s sails four minutes before half-time.
Although they were forced to hang on at the end as Liverpool pushed for an equaliser, Klopp applauded Paul Lambert’s side for their performance.
“We should not forget Wolverhampton did really well,” the German added.
“They scored the first goal and then defended well, had their counter-attacks and a good plan. We should have played better, so that is a fair result.”
Wolverhampton-born Stearman shocked Anfield by netting his first goal of the season after 52 seconds, setting his side on their way to another giant-killing after they won at Stoke in the last round.
“It is incredible,” he said. “We knew we had to start fast because we knew they would come out the blocks.
“We didn’t start well last week so it was vital for us to be on the front foot and get a goal. It is an incredible feeling.
“You can see the celebrations. Look how many fans we have brought today and it will carry on later tonight. We are delighted to be in the next round.
“Don’t take anything away from our defensive display today. The work-rate the midfielders and the strikers put in protected us from way out. That was the game plan and we are delighted with how it went.”
Wolves midfielder Conor Coady, formerly of Liverpool, added: “We knew Liverpool were on a little bit of a bad run so it was up to us to take the game to them.
“We did that. We scored two outstanding goals. You can see the celebrations, it is incredible.
“Words can’t describe it, it’s what I wanted all week. It’s a special day for me and my family. The boys have come up trumps.
“We’ve got nothing to lose now. We will enjoy today and really kick on.”