The third place finish gave India its first medal of the Championship. The trio shot a combined score of 400 to pip hosts Italy, who finished fourth with a total of 398.
The team from Great Britain won the gold with a score of 414 while Russia claimed the silver, finishing on 406.
In the men's individual double trap event, which had two Rio Olympic quota places up for grabs, Asab was the best Indian in qualifying, finishing 12th with a score of 135.
In the junior men's double trap team featuring Jaisal Singh, Shardul Vihan and Ahvar Rizvi finished fourth with a combined score of 372. Italy, Russia and China won the gold, silver and bronze respectively.