Rai, fresh from his gold medal in the air pistol mixed event along with Heena Sidhu, could not make the final of the men's 10m air pistol and was placed ninth. The top eight make the cut.
Multiple medallist at top global events, including the World Championships and Asian Games, Rai shot a sequence of 94, 96, 96, 97, 95, and 94 to total 572.
He shot 95 in the penultimate 10-shot series and eventually dropped to 94 to bow out of the competition at the Dr Karni Singh Shooting ranges.
In the women's 10m air rifle, India's only hope Pooja Ghatkar finished ninth and failed to make the final.
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Ghatkar's series included scores of 101.5, 103.9, 102.2, and an improved 104.8 for a total of 412.4.
The lowest qualifying score was 412.5, by Norway's Malin Westerheim.
Ghatkar had opened India's medal tally in the World Cup Stage 1 earlier in the year, by winning a bronze in the same event.
In the men's skeet, Italys Riccardo Filippelli clinched the gold medal beating Ben Llewellin of Great Britain 4-3 in a shoot-off. Both were tied at 59 out of the allotted 60 shots in the final.
Argentina's Federico Gil finished third to claim the bronze, finishing with a score of 49.
This was Filippelli's second title at this range, having won a gold at the World Cup Stage 1 in February.
Earlier, in the men's 10m air pistol event, experienced Japanese Pistol shooter Matsuda added another gold medal to the one he won at the very same range a few months ago.
Matsuda, a former ISSF world champion in this event, shot two remarkable series midway through the final, adding a 10.5 -10.9 combination in the 6th series to the 10.5-10.7 he scored in the previous one.
Alongside Matsuda on the podium was Ukrainian sensation Pavlo Korostylov, competing in his second World Cup Final at the age of 19. He won the silver with 241.1 and a junior world record to boot.
Despite a remarkable second half of the match, Korostylov was not able to match Matuda's pace.
His more experienced Ukrainian teammate Oleh Omelchuk, completed the 10m air pistol men podium, taking bronze medal with 218.8 points and adding it to the World Cup Final Gold he won in Bangkok in 2008 and to the bronze he won in Munich in 2013.