After signing a pre-contract with Juventus in the fall of 1971, which would have made him the most expensive defender in history until that point, he suffered a horrendous knee injury and the transfer fell through.

On the international stage, Fazlagić made 19 appearances for Yugoslavia, earning his first cap in a European Championship qualification match on 31 March 1963 against Belgium (1–0).

He is especially known internationally for being the captain of Yugoslavia during the 1968 European Football Championship, where the side took silver after a tight loss to the home team Italy after a two-legged final at the Stadio Olimpico in Rome.

[1] In 1974, Fazlagić was named player-manager of FK Sarajevo, which he led for one season, eventually being transferred to the club's youth department in order to gain more coaching experience.

The pair led a talented team of youngsters, including the likes of Faruk Hadžibegić, Husref Musemić, Slaviša Vukičević, Predrag Pašić and Zijad Švrakić, to the Yugoslav First League title in 1985, thus becoming champions both as players and as managers.

The team, fielding many future European stars including Zvonimir Boban, Robert Prosinečki, Davor Šuker and Predrag Mijatović, lifted the trophy.