It was the first time since 2009 that Nestor has failed to reach the semifinals at the eight-team, year-end event.
"It's definitely frustrating,, but it was not from a lack of effort," said Nestor. "We tried everything we had and left it all out there. At the end of the day, we just didn't have enough."
Nestor, 40, and Mirnyi ended their two-year partnership on a losing note, with Nestor set to team from January with Bhupathi.
The doubles ace from Toronto got a taste of what to expect on court in 2013. The Indians dominated the second seeds 17 aces to two — with their last one coming on match point in the tiebreak final set.
Nestor had played on the winning team in four of the last five editions of the tour wrapup.
He and Mirnyi won the title undefeated last year in their first season together.
Nestor and Mirnyi, the reigning French Open winners, were never truly dominant against the underdogs with whom they stood 2-2 this season heading into the playoff match.
The contest was a one hour 53 minute struggle which ended without a break of serve.
But Nestor and Mirnyi went begging at break points, missing on all seven of their chances while Bhupathi and Bopanna went 0-for-4.
"They returned well and made more big shots on big points than we did," Nestor said. "They had some outright clean winners and outplayed us today.
"I missed a couple of backhands on key points and a volley that I normally wouldn't miss. If we had made any of those and gone up a set, who knows."
The first two sets each lasted for almost an hour as the powerhouse teams attempted to impose domination, The Indians saved break points in early service games but trailed 3-1 in the first-set tiebreaker before pulling ahead to seal the opening set.
Nestor and Mirnyi reversed their luck in the second set, winning that one in a decider thanks to a winning Mirnyi lob.
But the Indians ran away with the match-tiebreak third, reaching five match points as Nestor hit a volley into the net. Nestor's side saved a first break point on a volley error but went down to defeat on the second from the concluding ace.
Nestor ends the 2013 season with 80 career doubles titles, including a repeat of Roland Garros honours with Mirnyi.
"Any time you win a Grand Slam, that's successful," Nestor said. "But I realize we've not won two matches in a row since Queens' (in June). That's a bit disappointing."