That advantage was wiped out within eight minutes as City ran away with it, closing the gap to Arsenal at five points.
Tottenham meanwhile have won just one Premier League match since the World Cup, and trail Newcastle in fourth by five points having played a game more.
Conte’s future in north London remains uncertain, with his contract up at the end of the season but the club do have an option to extend it by a further 12 months.
Speaking after the defeat to City, Conte made it clear that any demands he has made of the club so far in his time in charge are not even close to when he was managing elsewhere.
“If I demanded the same level as at Juventus and Inter it could be dangerous, as my frustration could be very big,” Conte told reporters.
“Instead I know what is my task in this situation and then I’m working very hard because I want to improve. I want to improve the team and the club with my vision, with my idea, with my suggestions. Then for sure we see.”
Asked what Tottenham needed to do to close the gap to those above them, he responded: “This is not a question for me. This is a question for the club.”
Goals from Dejan Kulusevsky and Emerson Royal put Tottenham in control after 45 minutes, though a rare first-half lead proved to count for little.
Spurs have now conceded two or more goals in nine of their last nine League matches, with their defensive record at this stage of the season the club’s worst since the 2007/08 campaign.
“Today we played a good game, we played with personality, we put a lot of pressure on them,” Conte said.
“At the same time, I’m disappointed. This is the first time in my career that my team concedes four goals in one half.
“We have to continue to work and try to improve this group of players. When I tell you that we have to reduce the gap, the process has just started.
“You have to work, to continue to work and improve technically, tactically and the experience of our team.”
He added: “These games are important for us to understand the difference between us and the other top clubs. We have a lot of difference in this moment but we are ready to work and to fight.”