He began his coaching career in 1991 leading the Partizan's youth squad, before being promoted to second assistant for the Partizan full squad. In 1994, he was named lead assistant coach for Beovuk before advancing to become the club's head coach for two seasons (1997–98 and 1999).
In 1999, Džikić was named assistant coach at KK Partizan, assisting head coach Nenad Trajković. Darko Russo took over the head coaching post in summer 2000 while Džikić remained the assistant. In summer 2001 Duško Vujošević returned as the head coach of Partizan, and Džikić once again continued in his assistant role, helping the team to four consecutive Serbia and Montenegro league titles from 2002 to 2005.
While working at Partizan under Vujošević, Džikić got his first taste of the NBA through Summer League coaching stints with San Antonio Spurs in 2003, Seattle SuperSonics in 2004, and Minnesota Timberwolves in 2005.
After completing his 2005 Summer League coaching stint with the club at Target Center, in August 2005, Minnesota Timberwolves offered Džikić an assistant coaching position on their staff, which he accepted. He thus became the first NBA assistant coach with no prior coaching experience in the United States at either the collegiate or professional level. Additionally, he became just the second European native to become an NBA assistant coach, after Igor Kokoškov became assistant coach on the Los Angeles Clippers staff in 2000.
In late 2007 he went back to Europe.
On 7 January 2008, after spending two and half years in the United States, Džikić became head coach of Slovenian team KK Union Olimpija.
Olimpija Union dismissed him in December 2008, after bad results in Adriatic League and EuroLeague and was replaced by Jure Zdovc.
On 15 July 2009, he became head coach of KK Krka in Slovenia.
In his first season, Krka did not compete in Adriatic League thus fully focusing on the domestic league in Slovenia from the start of the season. Džikić led the club to the Premier A Slovenian League title, the club's third in history, beating his old club Olimpija 3–2 in the playoff final series.
In the following 2010–11 season, he added to his success with Krka. Following the 17–9 regular season, they made the Adriatic League final four in Ljubljana where they lost to old rivals Olimpija. Some ten days later Krka won the 2010–11 FIBA EuroChallenge, defeating PBC Lokomotiv-Kuban in the final. Finally, they repeated as champions of Slovenian Basketball League. Soon after the successful seasons with Krka, richer European clubs, like BC Khimki, expressed interest in his services. He returned to Krka in June 2013.
In July 2011 Džikić was named the head coach of Lithuanian team BC Lietuvos rytas. In his first season at the club, the team came runners-up in the domestic league, losing the playoff final 0-3 to Žalgiris. The club recorded significant success on the European stage - following the heartbreak of missing out on EuroLeague due to losing versus Galatasaray at the last stage of qualifying tournament, the team responded by making the Eurocup final-four where they lost the semi-final to Valencia before winning the third place match over Spartak Saint Petersburg. Lietuvos rytas also took part in two regional competitions: VTB United League where they made the final-four, losing the semi-final to powerhouse CSKA Moscow and also the Baltic Basketball League, which they joined at the playoff stage and made the final that they lost to Žalgiris.
On 12 October 2012, he had part ways with the team.
In 2013, Džikić returned to be a head coach of the Slovenian team Krka. In June 2015, he left Krka.
On January 5, 2016, he was named a head coach of the Serbian team Partizan Belgrade, following the departure of Petar Božić. On June 13, 2017, he parted ways with Partizan.
On June 22, 2017, Džikić was named as the head coach of Budućnost Podgorica.
On 4 May 2011, Džikić got named the head coach of Serbian under-20 national team, in parallel with his club coaching duties at Krka.
In July he led the team at the 16-squad 2011 European under-20 Championship in Bilbao, Spain where they got eliminated at the group stage after recording a win versus Russia in the opening game, which was followed by two blowout losses, to Montenegro and Slovenia. This sent the team to the 13th to 16th place classification round with Lithuania, Croatia and Austria with knowledge that bottom two teams would be relegated to European under-20 B division. Džikić's team finally got their act together, recording six assured wins to stay in the A division.
The following summer Džikić led the team at the 2012 European under-20 Championship in Slovenia.
On 31 December 2013 Džikić got named head coach of the Macedonia national basketball team, succeeding Aleš Pipan in the job.
Džikić and his wife, Lilly, have a daughter Katarina.