The two-time defending Premier League champions were unable to secure three points at the Etihad Stadium on Saturday night despite playing at a higher level overall than Mauricio Pochettino's men, Efe news reports.
The key figure of the match was French goalkeeper Hugo Lloris, who broke up numerous chances created by the local side, while at the other end of the field the Spurs' attackers were opportunistic in turning scoring opportunities into goals.
The Citizens revved up their attack over a 15-minute stretch of the first half thanks to the play of Kevin De Bruyne, who set up both of the home team's goals.
The first came in the 20th minute when a curving pass from outside the area by the Belgian midfielder found Raheem Sterling, who got behind Tottenham's defenders and headed the ball inside the far post from close range.
Spurs, however, struck back just three minutes later on an accurate shot from outside the area by Erik Lamela, who had been set up by a pass from Tanguy Ndombele.
Manchester City took the lead back once again though on another play facilitated by De Bruyne, who sent in a ball from the right side that Sergio Aguero managed to poke into the left half of the goal past Lloris in the 35th minute.
That advantage lasted around 20 minutes, but Tottenham managed to equalize a second time in minute 56 on a header by Lucas Moura, who scored off a corner kick sent in by Lamela just seconds after entering the game as a substitute.
Manchester City head coach Pep Guardiola opted to make a change shortly after the half-hour mark and send on Gabriel Jesus in place of Aguero, who promptly got into a heated sideline argument with the former FC Barcelona and Bayern Munich manager.
Jesus appeared to give City the win when he scored after a corner kick in second-half stoppage time, but the VAR system ruled that French defender Aymeric Laporte had touched the ball with his arm before it got to the Brazilian forward.
Afterward, the Manchester City head coach praised his team's performance.
"We played incredible," Guardiola said. "One of the best games we've played in our time together. We played good, but unfortunately we could not win. We'll recover, train and prepare for the next game. We don't have regrets. That's the most important thing."
Manchester City (four points) are currently third in the Premier League standings behind Liverpool and Arsenal, who have six points apiece after two games.
Tottenham (four points) provisionally stand in fifth place, behind City and Brighton & Hove Albion based on goal differential.
( With inputs from IANS )