The former defender was impressed by how compact they were against Tottenham Hotspur on Saturday.
The former Borussia Dortmund manager took charge of the side for the first time since replacing Brendan Rodgers at Anfield, overseeing a 0-0 draw with Tottenham at White Hart Lane.
Many were keen to see how they would fare in the German's first game and were instantly impressed by what they saw, as the side noticeably pressed harder and employed Klopp’s famous geggenpressing from the outset.
And Carragher says it is clear to see he has made an impact on the side already.
“Very rarely do you see a manager stamp his authority on a team from day one, and that's what he did," he told Sky Sports.
"What I liked was how compact they were at White Hart Lane, 30 to 35 metres from back to front. He played in the positions they were suited to and still got them to press. The work from those first two to three days on the training ground was clear to see on the pitch."
The defender also believes that if Liverpool continue pressing as they have done, then the side are quickly going to become one that teams will not fancy coming up against.
The Reds were often criticised during Rodgers’ reign for developing something of a soft belly, with the number of goals his teams conceded something that came back to haunt his side time and time again.
The new high pressing somewhat eased the pressure on that defence on Saturday though, and Carragher says that if they continue to do it, it will not be an enjoyable game against them as it’s like they have another man.
'It's not going to be an enjoyable game playing against Liverpool now if they continue to press like that. And they will,” he added.
“It's like Liverpool having an extra man on the pitch in terms of pressing and defending. He's come in on day one and they've had more sprints and covered more distance than everyone else. If it was that easy, why doesn't everyone do it?”