Their six-wicket victory in Sydney ensured the hosts clinched the series 3-1, rallying after an emphatic 295-run defeat in the first game at Perth.
The bulk of the Australian side has been together for years and beating India remained an elusive goal for many of them.
Only Steve Smith, Nathan Lyon and Mitchell Starc were part of the squad that played in the last series win over their arch-rivals a decade ago.
Cummins said he was "immensely proud" of what his side had achieved.
"Obviously in the context of this series, it's been a massive series," he said after his 20th win as captain.
"It is one that a few of us didn't have. The boys have had their eye on it and it has lived up to the hype.
"We've spent a lot of time together as a group over the years, so we knew we weren't at our best at Perth.
"But it was never as bad as it seems. So you stick tight and double down on what makes us a really good side."
The victory ensured Australia will be at Lord's to defend the World Test Championship against South Africa in June.
"It's such a special group, we have so much fun," added Cummins of the squad.
"I feel so privileged to first of all have this job.
"But what we've been able to achieve together alongside the support staff as well, it's such a group effort, families as well. They give up so much. So yeah, really proud."
Australia handed out three debuts during the series -- opener Nathan McSweeney who was axed after the first three Tests, the man who replaced him, Sam Konstas, and all-rounder Beau Webster in the fifth Test.
They also heavily relied on stalwarts such as Smith, Starc and Travis Head.
"Always nice to have a squad," said Cummins.
"The three debutants in this series fitted in well. They contributed in different times.
"There were some key moments when our mainstays really stood up. You need to do that to beat a side like India."
