Virat Kohli celebrates India's win with his teammates after defeating Australia by 31 runs.
The India skipper said he believed his team collectively were better than Australia and deserved to win.
Virat Kohli said on Monday it was "very special" to captain India to their first Test win in Australia for a decade and gave his side crucial momentum in their bid for a maiden series victory.
The visitors won a tightly-contested opening Test in Adelaide by 31 runs on the fifth day after setting Australia a target of 323, which would have been a record run chase at the ground.
It was a big breakthrough for Kohli's men, with their last triumph on Australian soil at the WACA Ground in Perth in 2008. In Adelaide, their sole previous win was in 2003.
"Obviously it's a great feeling. We've never taken a lead in a series in Australia, something that for us is a huge boost," he said.
"And it's given us the right momentum that we needed to play a big series like this and it's something that we've had to work hard for.
"Any Test victory is special because you work hard over five days, and then the physical and the mental toil and the emotion of it all comes together in a result is a very special feeling."
Kohli, who has long led India's batting charge with admirable consistency across all three formats but failed to fire in Adelaide, said he believed his team collectively were better than Australia and deserved to win. The victory was built on Cheteshwar Pujara's first innings 123 and his second innings 71, while wicketkeeper Rishabh Pant took a world record-equalling 11 catches.
"It was priceless from Pujara, we were down and out at lunch on day one. His grit and determination brought us back in it," said Kohli.
"We always knew that runs on the board would make the home side tentative. Any lead was gold and we got 15. In the second innings again, he and Rahane batted well."
Asked if thought 323 would be enough to win, Kohli said his middle and lower order could have done better after a 5-25 collapse at the end of the second innings. "We could have added another 30-35 runs more could have taken the game beyond Australia."