Klopp's side fell apart after a blunder from Reds goalkeeper Adam Bogdan was punished by Watford's Nathan Ake in the third minute at Vicarage Road on Sunday.
Showing little resistance against tenacious opponents, Liverpool conceded a sloppy second goal when Odion Ighalo bullied Martin Skrtel into another mistake in the 15th minute.
Liverpool never threatened a response as Watford wrapped up their first home win over the Reds since 1986 when in-form Ighalo headed home in the closing minutes.
It was the heaviest defeat of Klopp's two-month reign and by far the worst performance.
Coming after praise was heaped on the German and his players following impressive wins at Manchester City and Southampton, Klopp wants to see what kind of response Liverpool, without a win in four matches, can summon now the going is a little tougher.
"After Southampton and Manchester City everyone thought 'wow'. That was one part of what we can do. Now everyone saw the complete other side," Klopp said.
"Maybe the truth is somewhere in the middle, but I know how strong this team can be.
"We don't feel good today of course. We came here to do something really different from what you saw.
"We have a few days before the next game and we will work on it.
"The easy game everyone wins. Now we have to win the difficult ones."
Klopp had no qualms about criticising Bogdan for his mistake, but he felt referee Mark Clattenburg could have blown for a foul before Ake scored because he virtually kicked the ball out of the goalkeeper's hands.
"We made bigger faults than the ref but in my opinion he had both hands on the ball so it is a foul," Klopp said.
"Mistakes can happen, that is football, but the reaction has to be better. We lost our minds after the goal.
"I would say hopefully it's the most disappointing moment in my whole Liverpool FC life."
- Soft touch -
Liverpool looked a soft touch without powerful Belgian striker Christian Benteke, who Klopp dropped to recall Roberto Firmino.
Benteke has been linked with a January move to Chelsea, but Klopp insisted there was no chance the former Aston Villa star would be sold just six months after moving to Anfield.
"That is the next problem. If you lose the games everyone is allowed to ask why didn't you play this or that player," he said.
"If it is the same probability as all the other transfer rumours Ive read since I've been here then I'd say I'm pretty cool."
While Klopp contemplates how to get Liverpool back on track, Watford manager Quique Sanchez Flores was basking in the glow of his impressive side's most complete performance of a remarkable first half of the season.
In their first Premier League campaign for eight years, Watford have defied the pundits who tipped them for relegation and head into the Christmas period only one point off the top four.
But Flores is determined to ensure his players don't rest on their laurels.
"We are playing against amazing players and managers and we are playing the way I want. I'm very happy," he said.
"It's very good for the Premier League what teams like Leicester, Bournemouth and Watford are doing. Every single weekend you don't know what will happen.
"But it would be a very big mistake to think about anything else other than trying to grow.
"We need to establish ourselves in the Premier League."
Flores also played down speculation that Nigeria forward Ighalo could be lured away from Watford by a bigger club in January.
"I think Ighalo is clever. He will stay with Watford, Why? Because it is something special for him I hope," he said.
"Something went wrong. I have to think about it again. It was a mistake and I will learn from it.
"I don't blame the referee or anyone else."