During his 18-year professional career, Subasic played for 15 clubs in 8 countries, mostly in Azerbaijan, Serbia and Turkey.

Subasic played for the Azerbaijan national football team between 2007 and 2013, scoring 7 goals in 40 games.

In 2005, he moved to Russian Premier League club Amkar Perm on loan where he played 6 games and scored one goal.

In his first appearance against Anderlecht in the UEFA Cup he gained a penalty and helped his team to have a victory with score 1–0.

Subašić joined Gabala FC at the beginning of the 2010–11 Azerbaijan Premier League season.

When the second part of the Premier League began Subašić started to play as the attacking midfielder.

Overall Subašić played 19 games in which he scored 2 goals and left Gabala in the end of the season because of the expired contract.

After leaving Gabala, Subašić moved to Khazar Lankaran at the beginning of the 2011–12 Azerbaijan Premier League season.

In the 2012–13 UEFA Europa League Khazar Lankaran played against JK Nõmme Kalju.

In June Subašić signed a 2-year deal with Turkish club Orduspor, playing in the TFF First League.

Subašić became one of the main players of Orduspor and played in the centre forward position in the starting squad in almost all of the games.

In July 2014, Subašić determined his contract with Orduspor and transferred to another Turkish club, Manisaspor.

He started his international career for Azerbaijan in March 2007 during Alma TV Cup.