Superstar paceman Bumrah was named player of the series for taking 32 wickets at 13.06 in one of the most dominant showings from a visiting quick to Australia in history.
But a back injury forced the stand-in captain to watch from the pavilion as Australia chased down 162 runs to reclaim the trophy on day three of a dramatic fifth Test in Sydney.
The game was in the balance when Bumrah left on day two, changing out of his whites to go for scans behind an ambulance escort.
He never returned to bowl and only batted briefly on day three as India posted 157 runs in their second innings.
Australia eventually made light work of the chase in reply, having been gifted a fast start by some wayward Indian bowling.
Beau Webster and Travis Head forged an unbroken series-winning 58-run partnership with six wickets in hand.
Jasprit Bumrah in action on day one of the fifth Test. (Dan Himbrechts/AAP PHOTOS)
India would have tied the series 2-2 with a win in Sydney and left with the trophy for a fifth consecutive time, but Indian coach Gautam Gambhir would not speculate as to what might have been had the talismanic Bumrah finished the game.
"I don't want to say that because Jasprit Bumrah wasn't there we couldn't get the result," he said.
"Obviously we had our moments and it would've been nice if he would've been there.
"But we still had five bowlers and a good team is one which is not dependent on one individual. We didn't get the result, as simple as it can get. We lost the series."
Clearly the most consistent player involved in the five Tests, Bumrah became only the second Indian to win the individual award in a losing series, after the legendary Sachin Tendulkar in 1999/2000.
But the 31-year-old seemingly ran himself into the ground as he carried India's bowling attack amid frequent changes.
He bowled 151 overs for the series, more than any other Indian player.
"A little frustrating but sometimes you have to respect your body. You can't fight your body," Bumrah said after the SCG Test.
"A little disappointing that I probably missed out on the spiciest wicket of the series but that's the way it is."
Scott Boland was named player of the match following his second innings haul of 6-47. (Dan Himbrechts/AAP PHOTOS)
Bumrah's fitness had been the subject of interest throughout the summer, with the 31-year-old previously having to overcome a groin complaint during the second Test in Adelaide last month.
He could be overheard telling then-skipper Rohit Sharma on day four in Melbourne: "Enough now, I'm not able to push more."
India's captain remained in the pavilion after lunch on Sunday, ruling out any chance of him returning to bowl.
Rival captain Pat Cummins conceded Australia's job was made easier by not having to face up to Bumrah, who dismissed each of the hosts' top-seven batters this series bar recent debutant Beau Webster.
"Every time he bowled he seemed to have an impact and took some key wickets. No doubt (his absence) helped our chase a little bit," he said.
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