Heinrich Retschury played for First Vienna FC as defender. Together with Wilhelm Eipeldauer he formed the defence of the club. He also played in the Austrian national footballteam. His first match was a 4:0 win against Transleithanien (Hungarian part of the Austrian-Hungary Empire). He played another 5 times in the team . His last match was a 1:8 versus England on June,1st 1909. Later he was member of the Olympic squad for the Stockholm Olympic games in 1912, but he did not play.