Army's Jitu, bronze medalist at Incheon Asian Games in the event in 2014, shot an overall 78.7 to finish eighth in the field of eight finalists to become the first shooter to crash out of the final round.
The 28-year-old got off to a poor start and could not recover from it in a highly competitive line-up, which included the likes of Hoang Xuan Vinh, Pang Wei, Wu Felipe Almeida, Tuzinsky Juraj, Jin Jongoh, Gontcharov Vladimira and Giordona Giuseppe.
After taking three shots, Jitu could only reach a total of 28.9. He followed it up with another poor shot of 9.7 to remain at the bottom of the heap.
Jitu desperately needed a qualify shot to avoid elimination but a shot of 10.1 in the end could not help his cause and he became the first shooter to walk out of the final round.
He had to overcome a deficit of 0.7 points against Gontcharov. Shot 10.1 in his last shot, and Gontcharov scores 9.7. So loses out by 0.3. His overall score 78.7.
Vietnam's Vinh finished with the gold with 202.5, while Almeida of Brazil took the silver and China's Wei settled for bronze.
Jitu is now left with another event in the Olympic Games -- 50m pistol, which is his forte.
Earlier in day, Jitu was impressive to qualify for the finals. He fired his way to 580 points with sequence of 96 in the first two series followed by 98, 96, 96 and 98. He shot 22 X to finish sixth out of 46 competitors in the qualification round.
However, Gurpreet Singh, India's other participant in the same category, failed to advance.
IMAGE: Indian shooter Jitu Rai
Rio 2016: I'm a soft target and people want to take potshots at me, says Paes
Rupinder's brace helps India edge past Ireland in hockey opener
TT: Mouma, Manika bow out after preliminary round defeats
Rio bomb squad blows up backpack near cycling course - official
Olympics: Shooters Chandela, Paul crash out in qualification round