"I said before that we are the second best side in the world," Ganguly said.
"But if we can win this series then we definitely can (be number one)."
Despite possessing one of the most talented teams in world cricket, India languish in sixth spot on the ICC world rankings because of their poor away record.
They had not won a Test in Australia for 22 years before Tuesday's breakthrough and had won just six of their last 69 Tests away from India.
"We are almost unbeatable at home but we haven't played well overseas," said Ganguly.
"We've started to play well over the last two years but we also knew we had to do something special to beat this side (Australia)."
India seemed to have no hope of winning the match after Australia racked up a daunting first innings of 556, then reduced the tourists to 85 for four.
But they turned the match around with a 303-run partnership by vice-captain Rahul Dravid (233) and Vangipurappu Laxman to get within 33 runs of Australia before Ajit Agarkar took six for 41 to skittle the home team for 196.
"This was our Test. I think we played better than them in the last three days of the Test and deserved to win," Ganguly added.
"There are some characters in the side, they may not look like it from the outside but they're pretty tough characters."
Ganguly, though, expected the Australians to come back hard.
"We have to lift out game, this is a four-Test series not a three-Test series. We know that they're going to come hard at us but also we know that we can beat them."
India, in a similarly unlikely performance, came back from the dead to win the second Test at home two years ago before taking the series 2-1.
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