Klopp's line-up featured three teenagers and right-back Connor Randall starting his first game of the season, a selection which resulted in a third consecutive home defeat in the space of eight days.
A home loss to Swansea all but ended Liverpool's hopes of catching Premier League leaders Chelsea, while Southampton won at Anfield in the League Cup semi-finals in midweek.
Liverpool must now face Chelsea in the Premier League on Tuesday, fixture congestion which goes some way to explaining why Klopp chose such a weakened line-up against Wolves.
"I'm responsible, I feel responsible for this performance," Klopp said. "I thought we could do better and obviously we couldn't.
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"I have to think about this, learn about situations, players and all games. It was an important game for us and we couldn't deliver.
"I was asked if it is the low point of my Liverpool time until now and I don't know if it is.
"But if it is, it's a perfect point to turn around because it is not possible to go lower. It is absolutely right that it feels bad.
"I am responsible for the bad things. We could have played better. Each boy could have played better. For each single performance there is an explanation.
- Damning -
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Lineker was particularly damning of Klopp's approach to the FA Cup, a competition Liverpool have won seven times in their illustrious history.
"Don't get Klopp playing his reserves with no European football," said Lineker via Twitter.
"Shows a lack of knowledge of the depth in English football and respect."
But Klopp refused to be critical of any of his youngsters, or the handful of senior players who lined up alongside them.
"We played a Championship team at Derby in the (League) cup and they had not a percentage of a chance. That is not years ago," Klopp said.
"It is not right to judge people in a very bad moment. It is not about not wanting, it is about not getting the right players in the transfer window.
"We have to go through the history of Liverpool, better sides lost against worse sides. We know what we have to change, only we have to show it.
Richard Stearman headed Wolves in front inside the opening minute before Andreas Weimann doubled Wolves' lead before the interval.
Not until the 86th minute could Liverpool finally break down Wolves' resilient defence, through Divock Origi, although the home side was unable to end their manager Paul Lambert's record of never having lost at Anfield, as player or manager.
"I've never been beaten here - that's with Celtic, Villa, Norwich - but that one is the best," Lambert said.