"We've won a few games and that's good, very good, but it doesn't change anything", Klopp said as Liverpool stayed at the top of the league after their fifth win from five games. "It was the moment where we could show that we are really convinced about what we are doing, we just had to do it more often and in a better way".
His manager, Mauricio Pochettino, is, refreshingly, not afraid to talk his players up (not so long ago he compared Spurs teenager Marcus Edwards to Lionel Messi). "Nobody plays a flawless season, not even City past year played a ideal season".
Erik Lamela pulled a goal back for Spurs but the Reds were not to be denied a fifth consecutive Premier League victory.
"I'm really happy and proud about the performance because the boys came back (from worldwide duty) only on Wednesday and Thursday", Klopp said. "His perception will be "wow" and the reality is you still need to prove it".
A ideal start through five games is not unheard of in the Premier League as Chelsea themselves have done it four times, though both of Liverpool's previous five-for-five came in the old First Division.
And Klopp is sure Kane will find his best form, even if he hopes it comes after Saturday.
"After that we had pretty good results and I don't think we conceded a lot of goals".
The German coach said his team would have lost if they'd been "5 percent less" with their performance, but they weren't and they won again as talk about them winning the title continues. "If he wants to take it, take it ... but of course his potential is to be a very, very good player for England and Tottenham, first for Tottenham and then if England believe that he can help them for England too", the Spurs manager added. "We deserved to win". "That is how it is, the body needs the time only to calm down from an intense season - they didn't have it". I don't like the situation, because I don't like to say to Fabinho, who is full of energy and desire to play, to tell him he is not involved. "We have seen that we can do it", Klopp said.