The Reds legend watched with interest on Saturday as the former Borussia Dortmund coach took charge of his opening match, at White Hart Lane.
Though the Barclays Premier League contest ended in a goalless stalemate, there were plenty of encouraging signs in the performance of Klopp’s team.
Carragher was certainly impressed and backed his former club to become a major nuisance to opponents if they can maintain that level of hard work.
He said: “I liked what I saw. Very rarely do you see a manager stamp his authority on a team from day one, but that’s what he did.
“Over the week since he’s had the job, we’ve been reading about what he is like as a manager – pressing, how much distance they are going to cover.
“Transition pressing was a massive thing for Klopp at Borussia Dortmund and it looks like it’s going to be a really big thing for this Liverpool team.
“One thing Klopp likes is for four or five players to get around the opposition player on the ball. He sees transition as a great opportunity to score a goal.
“As soon as they lose the ball you can see they will keep pressing until they win it back. They’re organised and you can see that has been worked on in the first two or three days in training.”
Carragher continued: “What was the difference? Well, these are things you don't see from every team. That is what impressed me in the past from Klopp and we’re seeing it from day one.
“The distance Liverpool covered, it was like they had an extra man on the pitch in terms of pressing and defending.
“The increase in sprints was the big one. The big thing in football is sports science and how quickly you can get to people and press people with high intensity.
“This was not a Liverpool team that were under the cosh or had 30 per cent possession, they had more possession than Spurs and they still covered that amount of ground.
“What I liked was how compact they were at White Hart Lane, 30 to 35 metres from back to front. He played them 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.”
Klopp’s options for his first fixture with Liverpool were limited by a series of injuries that struck the squad during the build-up to their trip to the capital.
Nevertheless, had Divock Origi’s header in the 10th minute snuck underneath the crossbar rather than against it, the boss may have been celebrating three points.
The striker was supported by the energy of Philippe Coutinho and Adam Lallana, who aided the midfield three behind them in continuously harassing Spurs.
“While Liverpool aren’t the only team to press in that way, it was brilliant to see such organisation on the first day,” Carragher added.
“The roles of Coutinho and Lallana were to stop balls going through the middle, they forced Tottenham wide all the time and they pressed. Despite having only three days to work with the team, you could see the organisation straight away.
“If you were to ask any of the Tottenham players whether they enjoyed playing in that game, I think it would have been a nightmare for them.
“Liverpool’s future opponents will be thinking they’re in for a right game, it’s going to be very tough and it’s not going to be enjoyable if they continue to press like that, and I think they will.

“I’ve heard it mentioned that all Liverpool have done is run around and that every team should do that. Every team doesn’t do that. You can’t continually throw that at Klopp, he’s come in from day one and he’s done it.”