The Brit Matthew Coward-Holley finished on 33/40 as Czech pair Jiri Liptak and David Kostelecky battled it out for the gold medal.
Although he Chelmsford shooter had arrived in Japan as one of the favorites for gold as the world and European champion but could not match the Czech duo.
However, the 26-year-old Coward-Holley has replicated the third place finish secured by Ed Ling at the Rio Games five years ago. As Liptak won gold and Kostelecky claimed silver after a dramatic shoot-off for the Olympic title.
Liptak would ultimately come out on top when Kostelecky missed his seventh shot. Coward-Holley had made a shaky start, making only seven of his opening 10 shots, but then responding with 14 in a row to get back on track.
That run ended just as early pace-setter Jorge Orozco Diaz began to falter, with the Mexican ultimately finishing fourth after missing three shots in a row during the elimination period.
With Kostelecky three shots clear at that point, Coward-Holley had been level pegging with Liptak but a miss in the 38th shot ended his hopes of progressing further.
Meanwhile, reflecting on his bronze medal, the Brit said: “It’s a little bit of a mix of emotions. I’m a little bit lost for words. It’s my first Olympics so to come away with a medal, it’s phenomenal.
“Being my first Olympic final, the first little bit of the final is always that little bit of tension, that little bit of nerves. But I thought, ‘you’ve got this far, you’ve just got to relax and trust yourself that you can do it’.”