World No. 8 Ayonika scored a creditable 417.7 but Apurvi Chandela (413.8) and Raj Choudhary (407.6) failed to come up with a better show and their combined total of 1239.1 left them at the sixth spot.
China rode on Siling YI, Binbin Zhang and Liuxi Wu to clinch the gold with an aggregate score of 1253.8, while the Iran team comprising Najmeh Khedmati, Narjes Andevari Emamgholinejad and Elaheh Ahmadi won the silver.
The 21-year-old Ayonika, who had clinched a silver medal in Commonwealth Games and also fetched a World Cup bronze in Slovenia, qualified for 10m rifle individual final but finished seventh after coming up with scores of 101.9.
The Indian was tied third with 30.8 after the first series but dropped to sixth place with 61.4 next. She remained tied sixth after the third series but by the end of the fourth series, Ayonika was out of the competition following shots of 9.7 and 10.5.