The 35-year-old was the last Indian shooting left at the Royal Artillery Barracks after Gagan Narang and Sanjeev Rajput had crashed out earlier in the day.
Sandhu finished with a score of 119 which was not enough to take him to the final.
Indian shooting contingent can be satisfied as they won two medals. Narang (bronze) and Vijay Kumar (silver) gave two medals for the country.
Indian women shooters drew a blank in this Olympics.
Sandhu had a sequence of 24, 24, 22, 25 and 24 on the second day of qualification.