Born in Šabac,[1] Srnić started his career with local club Mačva, before being acquired by Red Star Belgrade, along with his twin brother Slavoljub.[2] The twins joined the first team in 2010,[3] but Dragoljub failed to make any official senior appearance for the club. In order to gain experience, the twins were sent on dual registration to Serbian League Belgrade side Sopot.[4] In summer 2012, they both moved on a one-year loan to Čukarički.[5] Twins sued the club,[6] but later removed accusation and had been sold in 2013.[7]
Čukarički
In summer 2013, after a season-long loan in the Serbian First League, the Srnić brothers signed with Čukarički for an undisclosed fee.[7] In his first two seasons, Dragoljub played regularly and made 50 SuperLiga appearances and scored 1 goal. He also made 8 cup appearances, winning the competition in 2014–15, and 4 caps in the 2014–15 UEFA Europa League qualifications.[8] On 11 September 2015, Srnić scored both goals in 2–0 win over Radnik Surdulica in 9 fixture of the 2015–16 season.[9] At Čukarički, Srnić made 169 appearances and scored 6 goals in all competitions over five seasons.[8] He was also vice-captain to Igor Matić.[10] After the contract expired, he left the club in summer 2017.[11]
Śląsk Wrocław
On 4 July 2017, Srnić signed a two-year contract with Polish Ekstraklasa side Śląsk Wrocław, with an option for an extension.[12] He made his debut for new club in 2–0 defeat against Arka Gdynia on 16 July 2017.[8]