All four home strikes came from awful Liverpool defending, however, leaving their manager Juergen Klopp in the familiar position of trying to explain his side's porous rearguard.
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After nine games they are ninth, seven points behind Tottenham and 12 adrift of early pacesetters Manchester City.
"It was bad. Bad, bad, bad," the German coach said in the aftermath of a loss which brought Liverpool crashing down to earth after a 7-0 Champions League romp at Maribor in midweek.
"The first goal we had to clear the ball, the second goal Dejan (Lovren) missed the ball.... the third goal, another present. Everything that happened today was so obvious.
"Their desire was bigger than ours. How we defended in these four situations (goals) is not good enough."
If I was on the pitch in trainers their first goal wouldn't have happened.
Liverpool conceded twice in the first 12 minutes, one scored by Kane and one created by him for Son Heung-min, another in first-half stoppage time when Dele Alli punished a weak Joel Matip clearance and again early in the second half when Kane fired home after keeper Simon Mignolet flapped at a free kick.
For all their attacking verve, Liverpool have already let in 16 league goals, their worst record after nine games since 1964.
"That's not a nice statistic," Klopp, who reacted by substituting hapless central defender Lovren after 30 minutes at Wembley, told reporters, admitting that Lovren was not the only culprit in his side's capitulation.
"In all the decisive moments we were not there," Klopp said. "You can't get results with a performance like today.
"Spurs were completely spot on and we weren't. Now we have to realise we are responsible for this. Of course we can fix it, we have to fix it as well.
"The whole game the whole result was all our fault -- Tottenham were good, they needed to be good, but we made it much too easy for them."
The defeat leaves Liverpool in ninth in the league on 13 points after nine games.