Majority of his playing career was spent with FK Vojvodina, and he was also a member of the Yugoslavia squad that reached the final of 1968 European Championship.
Born during World War II in the city of Novi Sad that had been annexed months before his birth by the Kingdom of Hungary (that participated in the Nazi invasion of the Kingdom of Yugoslavia in early April 1941), Brzić's early life was spent under foreign military occupation.
He came up through all age levels in FK Vojvodina, but his senior career began with Sarajevo's FK Željezničar where he spent the first half of 1964-65 season. In December 1964, he returned to Vojvodina where he played next 8 seasons until summer 1972. He was an integral member of the squad that won the Yugoslav League in 1965-66 season.
He then transferred to Austrian Bundesliga where he played for Donawitzer SV Alpine and SK VÖEST Linz, where he began his coaching career.
His most notable coaching stints took place in Spain where he led RCD Mallorca, CA Osasuna, and Real Oviedo. He also coached Peruvian side Universitario de Deportes, Sport Boys, Alianza Lima. Austrian side Donawitzer SV Alpine and his home club FK Vojvodina.
In late September 2007 Brzić was named as new coach of FK Vojvodina after Milovan Rajevac resigned on September 17.
On May 29, 2008, it was announced that FK Vojvodina would not be extending his contract. Six days later it was announced that Dragoljub Bekvalac would be succeeding him on Vojvodina's bench.
FK Novi Sad 66-0