Career
Blažić started out with his local club Mladenovac. He made a name for himself at Čukarički, before transferring to in the winter of 2008, together with Pavle Ninkov. Blažić spent the following three years with the Red-Whites, before moving abroad to Slovak side Ružomberok in the winter of 2011.
He subsequently played for Russian club Amkar Permanent (2011–2012), as well as for Uzbekistani club (2013), and Kazakhstani club Atyrau (2014).
In July 2015, Blažić returned to his homeland by signing a one-year deal with Radnički Niš.