The Premier League champions endured an indifferent opening few months of their title defence as Manuel Pellegrini's men already sit five points adrift of leaders Chelsea.
Saturday's win over Spurs signalled City's third successive win, yet goalkeeper Hart is convinced that the best is still to come.
"We are building and have a lot more to offer this season. It was a difficult start but it's difficult for any top team," he told reporters.
"We are chasing Chelsea but we have our head down and focusing on Manchester City. We know if we do what we can do, we will be there or thereabouts."
Pellegrini's troops face two tricky away trips next. First, a trip to CSKA Moscow in the Champions League, before travelling to in-form West Ham United next weekend.