The 25-year-old Plantić lost the semi-final match to Russian athlete Artem Ageev who competed for Serbia. Ageev is one of seven Russians wearing Serbia's colours at the championships in Yerevan. He won the first medal for Serbia's boxing team back in 1991.
The bronze medal is Plantić's best career success after winning the junior European championships and second place in the junior world championships.
A total of 219 boxers from 39 countries competed in Yerevan and medals were won by boxers from 20 countries.
Croatia had five competitors at the championships - Luka Plantić, Petar Cetinić, Matteo Komadina, Marko Zeljko and Damir Plantić.