Guardiola’s side would have moved within two points of leaders Arsenal with a victory in north London, but Kane’s first-half strike - which made him Tottenham’s all-time leading scorer on 267 goals - left the Gunners firmly in control of the title race.
Second-placed City are five points behind Arsenal, who have a game in hand and host Guardiola’s men on Feb 15.
That will be a must-win clash for City if they are to have any hope of overhauling Mikel Arteta’s team, who had slipped up themselves on Saturday when struggling Everton snatched a shock 1-0 win against the Gunners.
Asked how frustrating it was to miss the chance to close the gap on Arsenal, Guardiola said: “Yes, of course, Arsenal have dropped few, few points so far and of course there was an opportunity.
“It was important to be close to Arsenal and leave the fifth place in the table, that Tottenham is right now, far away.
“We are not in the position to think about being champions.”
Tottenham’s plush new stadium has been a house of horrors for City since it opened in 2019.
They have lost on all five of their visits and are yet to score a single goal there.
After dominating possession in the early stages, City faded badly after Kane’s history-making goal.
With Kevin De Bruyne left on the bench for the first hour and Phil Foden absent from the squad due to illness, City lacked the creative quality to supply Erling Haaland with the kind of chance that Kane buried.
Haaland, well marshalled by Cristian Romero before the Tottenham defender’s late red card, failed to have a single attempt on goal for the first time since his move from Borussia Dortmund last season.
It was a worrying sight for Guardiola, who faced criticism for leaving out Belgium playmaker De Bruyne for what he called “tactical” reasons.
‘We are not the same’
With Joao Cancelo surprisingly allowed to join Bayern Munich on loan last week, Guardiola once again used teenager Rico Lewis at left-back.
Lewis has vast potential but his lack of experience in the role perfected by Cancelo as a defender with the licence to roam into midfield was apparent as Tottenham bypassed him with ease.
City’s third successive away defeat also raised questions about Guardiola’s faith in the underwhelming Jack Grealish and centre-backs Manuel Akanji and Nathan Ake - neither able to replicate the formidable presence provided by Ruben Dias and Aymeric Laporte, who were both among the unused substitutes.
Guardiola conceded his team’s latest inconsistent display was part of a worrying pattern City have been unable to stem throughout a campaign that threatens to fizzle out.
“Of course I have a lot of gratitude for these players. Always I try to do my best, I don’t want to drop much but I knew it,” he said.
“I said many times I knew we are not the same after winning a lot. Me included, I am the first to talk about that.
“It doesn’t matter what happened in the past or the success we had. No, we have to try to do it again. Now we are sad, tomorrow we will reflect.”
After winning four titles in the last five seasons, City look more vulnerable than at any time in Guardiola’s reign.
With their long-time rivals Liverpool languishing in 10th place, a changing of the guard in the Premier League could be looming.
Quizzed on his ability to battle with City and Liverpool for the major prizes when he was hired as Manchester United boss, Erik ten Hag suggested a shift in the balance of power was possible.
“I admire them both. They play fantastic football. Eras come to an end,” Ten Hag said.
Guardiola will hope Ten Hag’s bold prediction is not about to come true.
In yesterday’s other game Nottingham Forest eased their relegation fears with a crucial 1-0 win over Leeds United thanks to Brennan Johnson’s first-half strike.
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