Unlike Spurs' England contingent, Klopp has bedded captain Jordan Henderson slowly back into action, while Mohamed Salah and Sadio Mane's early exits in Russian Federation with Egypt and Senegal meant they had a few weeks of pre-season training.
"After that we had pretty good results and I don't think we conceded a lot of goals".
Goals from Gini Wijnaldum and Roberto Firmino gave the Anfield club the points, meaning that they have maintained their flawless start to the season.
Against Liverpool, he was substituted in the 73rd minute for Son, the South Korean making his first return since winning the recent Asian Games.
And Klopp is sure Kane will find his best form, even if he hopes it comes after Saturday.
The global break was long and arduous but with Premier League action set to resume today, supporters will be able to feast their eyes on the most exciting game of the week at Wembley. We had 85 brilliant minutes, although unfortunately we didn't finish the game off. Fantastic we won all of them, fantastic we improved during the season.
"I am long enough now in this business to know no one plays a flawless season - not even [Manchester] City past year played a ideal season", he said.
The only cloud hanging over an otherwise successful afternoon in London was an eye injury sustained by Firmino during a 75th-minute clash with Jan Vertonghen that saw Spurs awarded a free-kick.
Despite Liverpool sitting top of the Premier League, Klopp said it is not possible for the five-time European Cup winners to put off their Champions League campaign, which begins on Tuesday when Paris Saint-Germain visit Anfield.
"We have to go again in three days, not long for recovery, pretty quick", Klopp said. I don't know exactly at the moment, but it's something with his eye. "It's something to do with the eye and for sure it's uncomfortable for him", Klopp said. "But we will see".