Kostka participated in the 1972 Summer Olympics in Munich, where Poland won the men's football tournament.

Kostka is not only a successful player, he also was a manager, and graduated as a mining engineer from the Silesian Polytechnic in Gliwice.

His career began at small club LZS Markowice, but soon he was purchased by Unia Racibórz, and in the fall of 1960 he moved to Górnik Zabrze, a powerhouse of Polish football.

In the 1972 Summer Olympics, Kostka won the gold medal in the men's football tournament, but soon afterwards the aging goalkeeper was replaced by another star, Jan Tomaszewski.

He also helped Kazimierz Górski, Jacek Gmoch and Antoni Piechniczek with preparations for the 1970 FIFA World Cup.