Chain finished fourth with a score of 204.8 points in the final round. Gagan was second from bottom in the eight-man final with 142.3.
David Phelps of Wales won the gold medal with a new CWG record of 248.8. Neil Stirton of Scotland took silver with 247.7 while England's Kenneth Parr got the bronze with 226.6.
Earlier, Gagan finished the qualifying round in the third position with 617 points.
Chain was in sixth place, having scored a total of 614.2.
James Daly of Australia topped the standings in the qualification stage with 620.5 points.
Ryan Taylor of New Zealand was second with 619.4.
Gagan was consistent throughout the qualification round, starting off with 102.5 before shooting a superb 104.8 in his second attempt.
He bolstered his position with 102.3, 103.2 and 103.4 in his next three attempts.
However, a poor 100.8 in his final attempt ended his chances of finishing among the top two.
Chain meanwhile, had a superb start with 104.3, 104.2 and 103.1 in his opening three attempts.
However, he slipped down the standings with a 100.9.
He then managed an attempt of 102.3 before fizzling out with a below par 99.4 in his last shot.
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