[1] Brzić was born during World War II in the city of Novi Sad (then called Újvidék) that had been annexed just months before his birth by the Kingdom of Hungary.

Following the club's relegation to the Second League in 1964, Brzić moved to Željezničar Sarajevo, along with Lazar Lemić and Ilija Tojagić.

[4] After hanging up his boots, Brzić briefly worked as a coordinator in the youth system of Vojvodina before becoming an assistant to Branko Stanković with the seniors in 1977.

Between 1983 and 1986, Brzić was manager of La Liga side Osasuna, qualifying for European football for the first time in club history.

During the 1990s and early 2000s, Brzić spent several years in Peru, having stints with Universitario and Alianza Lima.