The Reds' dominance in the match finally paid off as Georginio Wijnaldum put his side ahead in the 39th minute after Tottenham failed to clear their lines from a corner kick played by James Milner.
This mature display was a real statement of intent by Liverpool, who have made their best start since 1990-91 as they chase a first English title since 1989-90.
"I'm not a personality to wait for problems, but I'm old enough to know they will come".
Liverpool blitzed Spurs early, creating two chances in the first three minutes with an opening goal being pulled back for Sadio Mané attempting a touch in an offside position.
After suffering four defeats against their top six rivals last season, including a 4-1 thrashing at Tottenham, this was exactly the kind of composed performance Klopp wanted to see.
Manager Mauricio Pochettino demands more desire as Tottenham prepare for Liverpool
We all need rest. "It's a massive lesson for everyone". "Like the man that he is, he's going to pay and accept everything". He added: 'Of course he's the first that regrets everything and all that happened yesterday is not good.
But Pochettino said after the match: "If you ask me if it was his mistake, I think it wasn't his mistake. Result is ideal and winning here is so hard, unbelievably difficult", Klopp said. Now we have to prove that and do it again and again and again.
"We will see, and then we play Paris Saint-Germain-they won yesterday without Neymar and Mbappe, so they can obviously rest players in the league". "It was a really outstanding performance that the boys delivered today. We had 85 brilliant minutes".
"We have had some fantastic players, the likes of Stevie [Gerrard], [Luis] Suarez and [Philippe] Coutinho, but now as a team everybody is right at it and that comes from the manager".
Writing in his column for BBC Sport, Lawrenson said: "Liverpool came unstuck against Spurs at Wembley last season but I have a feeling that both teams might cancel each other out this time".
And Wijnaldum has warned his team-mates they need to improve if they want to be closer this time around.
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