Srnić was molded in Red Star's youth system, and some observers in Serbian football had referred to young Slavoljub as "Ognjen Koroman's student".

Coach Aleksandar Kristić selected Srnić to make his professional debut for Red Star Belgrade on 6 November 2010 in a SuperLiga match against OFK Beograd.

During the loan spell at Čukarički from Red Star, Slavoljub was named by Mozzart Sport as the most valuable player of the Serbian First League.

[2] After the loan expired, Slavoljub and his brother refused to return to Red Star Belgrade,[3] and after many problems, they were sold to Čukarički in June 2013.

[9] On 29 January 2019, Srnić moved abroad for the first time in his career after agreeing to a two-and-a-half-year contract with Segunda División side UD Las Palmas.