Slavnić was one of the rare players who won everything he could in a career with his national team: 3 EuroBaskets (1973, 1975, 1977), the FIBA World Cup (1978), and Summer Olympics gold (1980).

Together with Dragan Kapičić, Duci Simonović, and Vladimir Cvetković, he was a member of one of greatest team in Red Star's history.

Unanimously, the executive board of the Serbian Basketball Federation, decided on 29 May 2007, that Slavnić should be the head coach of the first senior national team of Serbia; after the state union with Montenegro had ceased to exist.

[1] After numerous "thanks, but no thanks" decisions of experienced players, who didn't want to participate at EuroBasket 2007, Slavnić selected Milan Gurović, Marko Jarić, Darko Miličić, and nine debutantes, who later became standard members of the senior Serbian national team.

But, due to defeats to Russia, who went on to take the title, then Greece, who were the defending European champions, and won in overtime, and Israel, Serbia were eliminated in the first phase of the continental championship.