The 28-year-old Kane was missing from Spurs' squad for the match, but Tottenham did a "great job," according to Son Heung-Min, who scored the game's only goal in the second half to secure a surprise win.
The victory gave new Spurs manager Nuno Espirito Santo the perfect start, while the club's fans reveled in the win, chanting: "Are you watching Harry Kane."
Sunday's result also demonstrated why City might want to sign England international Kane.
"It was an incredible performance and everyone worked so hard to get these three points," Son told Sky Sports.
"Manchester City are currently the best team in the world so we fought for the three points and it means a lot to us at the start of the season."
Interviewed by Sky Sports after the match, the Spurs manager was asked about Kane's status, replying: "Harry Kane is one of the best players in the world, honestly. We are very lucky to have him. He has to get ready and help the team."
Tottenham have acquired the sobriquet "Spursy" -- a habit of flakiness and capitulation -- but there was nothing "Spursy" about this performance.
The London team's grit was typified by 22-year-old defender Japhet Tanganga, who was named man of the match after the way he nullified the threat of City forward Raheem Sterling.
"We allowed them too much, we could not control it, especially the simple thing when you lose the passes in certain positions it is always more difficult," City manager Pep Guardiola told the BBC.
"Football is goals, Son Heung-min scored the goal, we could not.
"It is normal for a season with not much preparation. The spirit was good but we lost. I am more than surprised how good we have done many things.
"A lot players arrived too late for Euros, for Covid, for many things. Players come back and every week will be better."
Guardiola's team featured Jack Grealish,
who was making his Premier League debut for City after the England international's $139 million transfer from Aston Villa earlier this month.
"He [Grealish] was excellent," Guardiola told the BBC." He played with a personality and created chances.
"Unfortunately we could not win for him for his debut but he played really well ... he doesn't lose the ball, he is so dangerous close to the box."