The hosts won back the trophy with their 2-0 lead going into the final Test in Sydney. Australia had finished their second innings at 318/9 at lunch and set India a target of 384 runs.
The visitors finished at 174/6 with R Ashwin and Mahendra Singh Dhoni holding ground. The Indian skipper later announced his retirement from Test cricket.
"It would have been nice to have won, that's for sure. But it's very satisfying to win the series and reclaim the trophy again. We had lost badly the last time but it was obviously in completely different conditions in India," said Smith.
Australia delayed their declaration in the morning, thanks to rain. It allowed Shaun Marsh to close on to a hundred but he couldn't finish the job as he was run-out on 99.
"It was obviously very disappointing for him," said the young skipper referring to Marsh's run-out.
"I ran out a message about 20 minutes earlier and said 'you have got until lunch'. I think that's when he started to go after the bowlers a little bit. He played very well, which is a very positive sign for us.