City had the better of the chances, including a missed lkay Gndoan penalty, before the Ukrainian received his marching orders in the 60th minute with scores at 0-0.
Within three minutes of the red card, Spurs took the lead through new signing Steven Bergwijn before Son Heung-Min added a second in the 71st minute.
“It was a key point,” Guardiola said about Zinchenko’s second yellow card.
“It was tough mentally for the team. We spoke to him at half time to be careful on yellow cards.
“To create more and concede a few, this is the only way I know.
“We played to win the game. I didn’t see a lack of desire to win or that were far away.”
City had 18 shots to three including five on target, while they also dominated possession with 67% of the ball.
Guardiola’s side also had almost twice as many passes as Tottenham but the Spaniard refused to criticise his players.
“How can I criticise my players?” Guardiola said.
“We played well, but we lost the game. They arrived twice and scored two goals. I don’t have too many things to say about our performance.”
The result means City remain second but are 22 points behind leaders Liverpool, which is the biggest lead in Premier League history.