The star quick bowler suffered a back niggle during the fifth Test in Sydney on Saturday and went for scans, ultimately forced to watch from the sidelines as Australia chased 162 to win.
He was the standout bowler, taking 32 wickets at 13.02 to be named player-of-the series, and his absence was a major blow to the team's hopes of retaining the Border-Gavaskar trophy.
"A little frustrating but sometimes you have to respect your body. You can't fight your body," he said after the six-wicket loss and 3-1 series defeat.
"A little disappointing that I probably missed out on the spiciest wicket of the series but that's the way it is.
"I felt a bit of discomfort during my second spell in the first innings."
India coach Gautam Gambhir said it was too early to assess the extent of the injury.
"Not at the moment, the medical team is working on it," he said, while praising his strike bowler.
"Absolutely outstanding," he said of Bumrah. "I can't say more than that. He led the attack really well, bowled a lot of overs and whenever he went out to bowl he did a fabulous job.
"But he was being helped a lot from the other end. There's been a lot of other contributions as well."
Mohammed Siraj and Prasidh Krishna led the attack on Sunday and while they did well, it was not enough.
- 'A lot of talent'-
Despite the defeat, India will take plenty of positives from the five Tests, with young opener Yashasvi Jaiswal further cementing his position in the side.
All-rounder Nitish Kumar Reddy impressed in his debut series, as did Washington Sundar, while Rishabh Pant proved once again why he is one of the most exciting players in the game.
"They've gained a lot of experience, they'll go from strength to strength," said Bumrah, captaining the side after the out-of-form Rohit Sharma "rested".
"We've shown that we have a lot of talent in our group. A lot of the youngsters are keen, they're disappointed that we haven't won but they'll take learnings from this experience."
Gambhir agreed there had been "a lot of positives".
"It's been really tough, they weren't the results we were expecting in these last three Test matches, but that is what sport is all about," he said.
"All I can expect from the dressing room is to keep fighting, that's all we can do ... we all play for results and it hasn't gone our way, it's as simple as it can be."
Reflecting on letting the series, and the decisive fifth Test, slip away, Bumrah added: "Lots of ifs and buts because the whole series was well fought.
"Today as well. We were in the game. It was not like it was totally one-sided.
"This is how Test series go in the nervy moments, whichever team holds their nerve for the longest time and sticks together will win the series.
"It was a well fought series, a lot of good learnings for us ... being in the game for longer, creating pressure and sometimes absorbing pressure when the wickets are difficult and sometimes playing to the situation."
