Born in Zagreb, he started playing with HAŠK before moving to Građanski Zagreb in 1942 where he became the substitute of Franjo Glaser for the following 3 seasons.

[1] In 1945 he moved to Belgrade and joined FK Partizan where he would play until 1949 making a total of 239 appearances (84 of which in the league)[2] and win two Yugoslav championships, in 1947 and 1949, and one Yugoslav Cup, in 1947.

Šoštarić made his debut for Yugoslavia in an October 1946 Balkan Cup match against Romania and earned a total of 18 caps, scoring no goals.

He was part of the Yugoslav squad at the 1948 Summer Olympics where Yugoslavia won the silver.

[3][4] His final international was a June 1951 friendly match against Switzerland.