The 28-year-old Asian Games gold medallist finished 12th in the six-series qualifying after being placed fourth at the end of the fifth and penultimate series at the Olympic Shooting Centre. Rai aggregated 554.
Defending champions Jin Jongoh of Korea topped the qualification with 567 and he was followed by Chinese Pang Wei (565) and Korean Han Seungwoo (562).
The other Indian participant in the event, Prakash Nanjappa, finished a lowly 25th out of 41 with an aggregate of 547 as the shooters continued to draw blanks from the ranges.
Scores of 90 94 were followed by another 95, including four 10s, in the fifth series that propelled him to the fourth position at the completion of the series.
However, the Army man botched things up completely in the final series that included two eights, which left him way behind in the pecking order. Not his usual self, a final effort of 10 was not enough for Jitu to avoid elimination in his maiden Olympics.