Nicknamed Zagi, Zagorčić played as a defender and began his career with FK Novi Sad.

In this time Zagorčić made his debut for the Bulgaria national team under manager Hristo Bonev prior to the 1998 World Cup.

In July 2006 Zagorčić joined the coaching staff of his former club Litex Lovech, as he was appointed assistant to manager Ljupko Petrović.

In the summer of 2013, he was appointed as manager of Litex, replacing Hristo Stoichkov, who had stepped down as head coach.

On 11 May 2017, Zagorčić was appointed as a manager of Slavia Sofia after the bad form of the team under Vladimir Ivanov.