Konstantinou was born on June 4, 1947 and played for Panathinaikos' youth team before becoming Takis Economopoulos' backup and understudy. He filled in successfully for his "mentor" when the situation called for it as was the case in the 1971 Champions' Cup semi-final against Crvena Zvezda (3-0) which sent PAO to the final. Eventually, Konstantinou became the first team's keeper, a position he held until the 1983 season. He ended his career in 1984, playing for OFI.
Konstantinou also had an interlude (1979) in which he played for Toronto of the North American Soccer League.