Smith has 'unfinished business' with England and India
The 31-year-old had an astonishing tour of England last year, blazing 774 runs from just four Tests, having missed the third Test with concussion after being hit by a Jofra Archer bouncer.
But his exploits were only enough for Tim Paine's side to retain the fabled Ashes urn as holders, rather than win it outright, with the series ending 2-2 after Australia lost the fifth and final Test at The Oval.
Smith said it left him disappointed and with "unfinished business".
"To know that we'd got the Ashes back was pretty special," he told The Unplayable Podcast this week. "Unfortunately, we couldn't win them which is something I'd still like to do.
"From my personal perspective, I think it's unfinished business," he added. "It's great to retain the Ashes but it just doesn't sit right with me when you don't win it. We drew the series -– good, but not great.
"So I probably left at the end of the fifth Test (feeling) more disappointed than a sense of achievement."
The last time Australia won an Ashes series in England was 2001 when Steve Waugh's men achieved the feat.
The two sides are scheduled to meet again in Australia next year before returning to England in mid-2023, when Smith will be 34.
A series win in India is another major driver for the former Australian captain, who has notched 7,227 runs in his 73 Tests so far, with 26 hundreds.
"They're the two big mountains to climb and if you can do that, it would be pretty special," said Smith, with winning a series in India eluding Australia since 2004.
"Hopefully I get another crack at it, we'll see how we go. I'm getting a bit old now. You never know how long I've got left, and you never know what the future holds.
"But it's certainly something to strive for, that's for sure."