Azinović started his professional career at his home townclubKalmar FF in 2005. He was the second choice behind Petter Wastå and made three appearances for the club in Allsvenskan. In 2010 both Azinović and Wastå were outrivaled by Etrit Berisha.
On 22 August 2012 it was announced that Azinović would transfer to Allsvenskan club Malmö FF with a short-term contract for the rest of the 2012 season. Azinović made no first team appearance for Malmö FF before the end of the season when it was announced that the club would not extend his contract. After a brief spell back at Kalmar Azinović returned to Malmö FF and signed a two-year contract on 9 January 2014. Azinović made two appearances for Malmö FF during the season, in the home fixture against Örebro SK on 13 August2014 and the final game of the season against Åtvidabergs FF on 1 November 2014. He announced his retirement from professional footballin the summer of 2016 following a serious injury.