The England international swept home from the penalty spot before Christian Eriksen struck Spurs' decisive second after Kelechi Iheanacho had drawn the home side level on Sunday.
Mauricio Pochettino's side are now just two points behind league leaders Leicester City and, while Kane insists they will not get carried away, the striker feels confidence is now sky-high within a squad still in the hunt to win three trophies.
When asked if he considered Spurs to be title challengers, he told Sky Sports: "That's up to you to decide - we know what we are capable of.
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"We feel we can beat anyone in the league and we fancy our chances against anyone.
"It was a very big game, away at City who are a top team. Everyone is fighting for places so to come away with a win is a good feeling.
"But there is a long way to go. We are in three competitions and are taking them all seriously. Coming here and getting three points will give us confidence.
"It was a good open game. We have to keep going and do the right things. We can't get carried away but it is a big away win."