Klopp's side made it five successive victories as goals from Georginio Wijnaldum and Roberto Firmino rewarded their dominant display at Wembley on Saturday.
A late goal from Erik Lamela proved to be just a consolation for Spurs, who were without captain Hugo Lloris and Dele Alli.
Spurs were looking to bounce back from losing at Watford prior to the worldwide break, however, his side never really got going against a slick, well oiled Liverpool machine that have won all five of their Premier League matches to date.
Lamela scored a consolation goal with a handsome volley after he found himself unmarked inside the box to give Liverpool a scare in the dying minutes of the game.
"I am long enough now in this business to know no one plays a flawless season - not even [Manchester] City a year ago played a ideal season", he said.
While Kane collected the Golden Boot in Russian Federation, the six goals came in his first three games and that was followed by a three-match barren run.
"We should be talking in a different way now because if it was given, it's 2-2 if we score the goal. We were that good it was hard for Tottenham".
But Pochettino said after the match: "If you ask me if it was his mistake, I think it wasn't his mistake".
"And we concede again in set pieces. Result is ideal and winning here is so hard, unbelievably difficult", Klopp said.
And Wijnaldum has warned his team-mates they need to improve if they want to be closer this time around. "It was a really outstanding performance that the boys delivered today". But we all have our 20 minutes.
The Reds head into the game looking to preserve their 100 per cent start to the new season after Jurgen Klopp's men won all four of their opening four games in the top flight. "Playing our football in that way that's really nice for a manager".
Klopp was cautious after the incident but refused to blame Vertonghen as he said he did not see the incident from his spot on the touchline.
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