Narang, a bronze medallist in the 2012 Games in the 10 metres Air Rifle, finished 13th in the qualification with a total of 623.1 points.
The 33-year-old scored 104.7, 104.4, 104.6, 103.0, 104.0 and 102.4 in the six series.
Chain was 36th with a total of 619.6 points. Chain posted scores of 104.1, 101.0, 104.4, 102.4, 103.9, 103.8 over six series.
The top eight shooters qualify for the finals. Russian Sergey Kamenesky topped the chart as he shattered the Olympic record with a score of 629.0 (103.9, 105.1, 106.0, 104.7, 105.2, 104.1).
Kirill Grigoryan took the second spot with 628.9 points, while South Korean Jonghyun Kim was third with 628.1 points.
Indian Gagan started off strongly as his 104.7 in the first series gave him a tied fourth spot and the following series of 104.4 put him in the third spot.
He moved down to the fifth spot after the third series with a 103.0 score. In the following series, he scored 103.0 to move down another three spots. He improved in the next series with a score of 104.0 but it was not enough for him to force his way up.
An average score of 102.4 in the sixth and final series pulled him further down to the 13th spot, ruling him out of the finals.
His compatriot, Chain also started strongly, putting a 104.1 but he failed recover after posting a score of 101.0 in the second series. A decent 104.4 was followed by a 102.4, taking him out of the top 30 spots.
Later, he posted scores of 103.9 and 103.8 in the fifth and sixth series to finish 36th.