Liverpool suffered their third consecutive home defeat in seven days after goals from Richard Stearman and Andreas Weimann saw Wolves take a shock 2-0 lead at Anfield on Saturday (28 January).
While Divock Origi pulled one back late on for the home side, a hugely underwhelming performance saw them eliminated from a second cup competition in four days, following their EFL Cup semi-final loss to Southampton on Wednesday.
Liverpool's week from hell started with a 3-2 defeat to Premier League strugglers Swansea City last Saturday (21 January).
Things do not get easier for Klopp's side with league leaders Chelsea coming to town on Tuesday, but the manager is hopeful his side can pick themselves up before then.
"It doesn't make it easier for Chelsea, that game is not decided already," Klopp said post-match, BBC Sport report. "It's up to us and if we play better we have a chance. If we don't, we don't have a chance but it is too early to talk about the next game. We have to talk about this game, but with the team not within public with you guys."
Klopp made nine changes to the side that lost to Southampton with Loris Karius and Roberto Firmino the only players to retain their places.
Philippe Coutinho was introduced off the bench at half-time with Daniel Sturridge also entering the fray later on, but they were unable to turn the tide.
Klopp sought to take full responsibility for the defeat.
"The start immediately gave them confidence, we obviously weren't ready," he told BT Sport. "We had the ball, gave it away, then a foul, a free-kick, the goal happened and then we tried but not well enough.
"In the second half it was better, but really it was not possible to be worse. I've not got a lot more to say. I am responsible for the line-up. I am not allowed to blame a single player. Of course, you see them and you learn a lot about them in situations like this too, but I am responsible."