Konstantinou was born on March 11, 1951 in Paleometocho, Cyprus. He played for EPA Larnaca winning top-scorer honours with them in 1970. He made the move to Greece and AEK Athens in 1973 and was a member of the team that won consecutive championships in 1978 and 1979. He ended his career with AEK in 1981.
During his playing career, Tasos was capped by the Cypriot National Football Team nine times scoring one goal.