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.
[7] In summer 2013, after a season-long loan in the Serbian First League, the Srnić brothers signed with Čukarički for an undisclosed fee.
[11] On 4 July 2017, Srnić signed a two-year contract with Polish Ekstraklasa side Śląsk Wrocław, with an option for an extension.