A brace from Connor Wickham helped the Black Cats come from behind to lead heading into the final five minutes at the Etihad Stadium, but Samir Nasri scored a late equaliser, ensuring that the two sides shared a 2-2 draw.
The manager told BBC Sport: "I haven't had the heart attack that football is trying to give me every game! We deserved better.
"We conceded a goal after two minutes at Manchester City and every single person in the world expected us to lose from there. But we passed the ball and create chances. We kept believing."
Despite picking up a point, Sunderland remain at the bottom of the Premier League table, six points from safety.