The Australians took the series 2-0, but plucky India held on for a second successive draw over five days in the final Test at the Sydney Cricket Ground.
This year's result is a turnaround for Australia after a humiliating 4-0 defeat by India on their home turf in 2013.
But Smith said the Aussies might have won by a greater margin if not for the unresponsive pitches and bungled catches.
Shaun Marsh's dropped catch on Saturday when Murali Vijay was on 42 – on the way to 80 – was Australia's 17th missed fielding opportunity in the series.
"I think the wickets have been extremely flat and it's been tough to take 20 wickets," he said.
"Throughout this season we've let ourselves down in the field. Perhaps if we had taken a few more chances, it might have been a little bit different.
"They are not the standards we set as an Australian cricket team.
"We have a lot of work to do on our fielding, with one-day series and the World Cup coming up, to get our standards up where we want them to be."
Australia won the opening two Tests in Adelaide and Brisbane, but could not take 20 Indian wickets in the remaining Tests in Melbourne and Sydney, which finished in draws.
"It has been tough to get 20 wickets in this Test series," he said.
"The wickets haven't broken up quite as much as we thought they would. I don't know the reasons for that.
"The bowlers have toiled extremely hard throughout these four Test matches and I'm really proud of the way they gone through these games."
It was a batsmen's series with a total of 15 centuries scored, four each to Smith and Indian counterpart Virat Kohli.
Smith finished as the player of the series. Apart from his hundreds he took some exceptional catches, none better than his brilliant flying right-handed grasp at second slip to dismiss Rohit Sharma for 39 on Saturday.
"It was just one of those ones. I think [former Australia Test captain] Mark Taylor talked to me about three he dropped in Adelaide," said Smith.
"He said 'they usually come in threes.' I said: 'Thanks for the confidence Mark.'
"I was just one of those ones, got across to it and it stuck."
Smith said he had enjoyed being captain for three Tests in the absence of Michael Clarke due to injury.
"I've really enjoyed it, I've had a great time." he said.
"A lot of the senior boys have been helping me out and the boys have done everything I've asked of them.
"They've worked their backsides off every day and I couldn't be prouder of them for the way they've performed in this series."
India must learn from Aussie bowlers to win more away Tests - Kohli
Virat Kohli said India must learn from Australia's bowlers if they are to improve as a Test side after holding the Australians to a draw in the final Sydney Test on Saturday.
Kohli, who took over the Test captaincy after Mahendra Singh Dhoni's shock retirement following the third Melbourne Test, said he was proud that India made Australia earn their 2-0 win in the four Test series.
"At the international level there is a lot for us to improve on as a Test side, especially seeing the way the Australians bowl. I think that's something we need to learn from big time," he said.
"If we can improve on that we're going to be a very strong Test team moving forward."
Kohli, who scored an Indian record series aggregate of 692 runs at 86.50 against Australia, said his team made the home side fight all the way.
"The result has not gone our way but we have played the kind of cricket that we wanted to and honestly Australia have had to earn both the victories they've had," he said.
"When we get more composure and improve on a few areas, you will see us cashing in on those important moments.
"What matters is they won the series. We did not. But the way we played in this series is something very exciting for us and something to look forward to in the future."
Kohli said India must learn from Australia's bowlers if they are to win Tests away from home.
India have won only one of their last 23 Tests overseas.
"Especially someone like Josh Hazlewood who has put the ball in the right spot in all three of his Test matches," Kohli said.
"That's something we need to work on big time if you want to take 20 wickets and win Test matches."
Kohli said it had been challenging yet enjoyable playing against a competitive Australian team in front of vocal crowds.
"I had a couple of incidents the last time but this time they (crowds) haven't been disrespectful," Kohli said.
"They have booed me but I know they have liked the way we have played our cricket.
"They have liked the way I go out there and annoy the opposition.
"To have the whole Australian crowd and 11 players who want to irritate me and get me out has been challenging but it has been enjoyable.
"It has brought out the best in me. This is certainly the best Test series that I have had so far.
"There were a lot of things that went on during the series but eventually we all shook hands.
"We respect the way they play and both teams know this was a strong fight and enjoyed it equally."
Like Sports on Facebook, follow @ETribuneSports on Twitter to stay informed and join in the conversation.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ