Liverpool's next Premier League fixture pits them against Chris Hughton's well-drilled Brighton side and three points will be the minimum requirement for Klopp.
The FA Cup defeat also condemned Liverpool to consecutive defeats for the first time this season, following their 2-1 league defeat to Manchester City, and it also meant that the side are now winless in the new calendar year.
Klopp handed debut's to youngsters Curtis Jones and Rafa Camacho, while 16-year-old Ki-Jana Hoever came on for the injured Dejan Lovren to make his first appearance for the club.
Klopp's critics were out in force following the 2-1 defeat at Wolves, with a lot of rival fans clearly very anxious this fine manager will bring the glory days back to Liverpool as he has built a wonderful team over the last three years.
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While City's success has to be seen as plasticised, Liverpool's will be very real if they build on a fantastic start to this season and end the club's long wait for a title success. "I think at the start of this season we weren't playing our best but we were getting results".
"The goals we conceded against Wolves were really poor", Aldridge wrote in his Liverpool Echo column.
"Klopp gave an opportunity to some senior pros who have been waiting for their chance but they wasted it".
Lovren went down with a hamstring problem and Klopp was unable to say how bad it was, but with Joe Gomez and Joel Matip already out it's vital that he gets back into the side as soon as possible. They played within themselves and that's not good enough. It was my mistake for the first goal and it's cost us, if not it's 1-1 and we get a replay.
"You certainly couldn't attach any blame to the young lads". Then Neves, with the wind in his back, hit a nice little shot.