During his career Ščasný earned four caps as a Czechoslovakia national team player, making his debut against Cyprus on 27 March 1983.

[1] Ščasný began his coaching career by acting as a player-coach at Anagennisi Dherynia, and he later supervised the youth there.

Ščasný returned to his homeland in 1993, and, after working with some smaller clubs, he became an assistant coach at Sparta Prague in 1996.

His work at OFI led Greek giants Panathinaikos to hire him early in the 2004–05 season to replace Itzhak Shum.

Ščasný took over in the middle of Panathinaikos' UEFA Champions League campaign, and with two impressive draws against Arsenal, another draw in Norway against Rosenborg and a resounding win over PSV Eindhoven in Athens, Ščasný guided the Greek side to finish 3rd in a difficult group, thus moving them to the UEFA Cup.

Before Panathinaikos began the UEFA Cup competition later that season though, Ščasný was replaced in favor of Alberto Malesani.

On 30 December 2010 Ščasný signed a two-year contract with Hungarian champions, Debreceni VSC.

In October 2012 Ščasný returned to Czech football after a three-year absence, taking over at FK Teplice.