Vukoičić was only 19 years old in 1994 when he began working as coach in KK FMP's youth system. He continued there until 2003 when he got promoted to the position of first teamassistant coach. Working under head coaches Aco Petrović, Vlade Đurović, and Boško Đokić, he gained valuable experience.
Vukoičić's first head coaching appointment came in 2005 at FMP where he ended up spending two and a half seasons. He won the 2005–06Adriatic League title with the club. Next year he led the team all the way to the semifinals of the 2006–07 ULEB Cup and also won the Serbian Cup. He was fired on January 14, 2008.
In early November 2008, Vukoičić agreed terms with KK Bosna, six days after the team's previous head coach Alen Abaz resigned in late October following a loss at KK Budućnost Podgorica in the Adriatic League. Goran Šehovac assumed temporary charge for one game, before Vukoičić took over with his Bosna debut taking place in Belgrade away at KK Crvena zvezda. Vukoičić led the Sarajevo team to the 7th place Adriatic League finish with an 11–15 overall win-loss season record. Under Vukoičić's command, KK Bosna had a 9–11 record. On 12 April 2009, following a Bosnia-Herzegovina league loss away at KK Borac Banja Luka, Vukoičić offered his resignation. It was not accepted, and he continued on as head coach. In late May 2009, during the Bosnian domestic league finals series, he signed a 4-year contract extension with the club. KK Bosna ended up losing the final series versus HKK Široki 0–2. Vukoičić started the 2009–10 season as head coach but got fired in early December 2009 following disastrous 1–9 start in the Adriatic League, including the embarrassing 50-point loss to KK Zadar.
Mega Vizura
In 2010, Vukoičić became head coach of KK Mega Vizura from Belgrade, that participates in the Basketball League of Serbia. In his first season with the club, Mega Vizura finished the season's initial stage in 4th spot with 15-11 record thus qualifying for the final stage of the competition. Superliga proved to be a step too far and Mega Vizura finished in last place with 3-11 record.
On October 4, 2012, he became head coach of the Serbian team Crvena zvezda, replacing recently fired Milivoje Lazić. Arriving to Crvena zvezda for Vukoičić meant getting reunited with Nebojša Čović whom he worked for over a decade in various capacities at FMP Železnik. Taking over the team that started the Adriatic League season with two straight losses away at Split and Zadar, Vukoičić won his debut match coaching Crvena zvezda at home versus Olimpija, which was followed by two losses, away at league favourites Boža Maljković-coached Cedevita and an upset loss at home versus Igokea. Vukoičić finally righted the ship as Crvena zvezda went on a 6-game win streak that included a win over eternal rivals Partizan. The streak ended in early December away at Budućnost, but the following week the team got back on tracking starting another winning streak this time for 5 games. Mid-January brought the away clash with league-leaders Igokea, which Red Star lost on a last second three-pointer by Siniša Štemberger. Vukoičić's team then went on another winning run of 5 games including yet another win over bitter city rivals Partizan. Crvena zvezda also won the Serbian Cup by beating Partizan for the third time in the season in the incident-filled final played over two days in Kragujevac. The team ended the season in second spot thus qualifying for the Final Four. In the meantime Serbian Superliga started, and Crvena zvezda opened the competition in disappointing fashion with loss to Partizan, hard-fought win versus Radnički, and an upset loss away at Mega Vizura. On 15 April, days after the Mega Vizura loss, Vukoičić's firing was announced while Dejan Radonjić who coached Adriatic League rivals KK Budućnost got named as replacement with club president Čović citing "obvious deterioration of form" as the reason for the change.
In 2007, Basketball Federation of Serbia named Vukoičić head coach of the Serbian under-20 national team for the upcoming European under-20 Championship in Slovenia and Italy. Coming into the tournament as the defending European champions, the Serbian team consisting of players born in 1987 was led by the talented combo guard Miloš Teodosić and power forward Dragan Labović both from FMP Železnik where they were also coached by Vukoičić in addition to small forward Milenko Tepić from Partizan, forward Nikola Dragović from UCLA, and center Marko Durković. Despite losing their opening game versus co-hosts Slovenia, Vukoičić's team quickly got on track, winning all their games until the end, including the final versus Spain and defending the title. Four years later in 2011, Vukoičić, now coaching Mega Vizura at club level, again got the call from his country, this time to coach the Serbian under-18 team at the Euro championships in Poland. Consisting of players born in 1993 with a few born in 1994, the squad made the final where they lost to Spain.
Serbia full squad assistant coach
In late summer 2012, ahead of the EuroBasket 2013 qualifying matches, Vukoičić joined the national team's coaching setup as one of the three assistants to Serbia national team's head coach Dušan Ivković. Serbia managed to qualify, though not without drama, unexpectedly losing 5 matches including to minnows Estonia, barely grabbing the third and final qualifying spot in its group through better basket difference.
