Bindra, the country's lone individual Olympic gold medallist, lost the shoot-off to Ukrainian Serhiy Kulish after both were tied for third place at 163.8 points following 16 shots.
Bindra, who was playing in his fifth and final Olympics, was deprived of a fairytale ending of his glorious career as he was the fifth shooter to be eliminated in the race for the podium.
The 33-year-old Indian, who won a gold in 2008 Beijing Olympics in the same event, was at the second spot at one time but lost places later on. He was fourth at first elimination round but jumped to second after the second elimination round.
Two mediocre shots took him to fourth spot after the fourth elimination round but he bounced back in the next round with scores of 10.6 and 10.2.
But that was not enough for Bindra to stay clear in the top three as he was tied at third spot with Kulish at 163.8 points.
Despite a strong backing of Indian supporters cheering him, Bindra just could not make it count in the shoot-off.
Italy's Niccolo Campriani, silver medalist in the London Games four years ago, won the gold while Kulish and Russian Vladimir Maslennikov took the silver and bronze respectively.
Bindra had scored 625.7 to book a berth in the finals. This is the only event Bindra is competing in the ongoing Olympics.
Bindra joined Apurvi Chandela, Ayonika Paul, Kynan Chenai and Manavjit Singh Sandhu, who have already exited from the shooting range, while Narang has two more events -- 50m rifle prone and 50m three position left.
Jitu Rai, who had exited in the 10m air pistol along with Gurpreet Singh, will be fighting in the 50m pistol. Gurpreet will also be seen in action in the 25m rapid fire.
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