Partizan were leading 2-1 when Vojvodina had an 80th minute goal ruled out. The disallowed effort came just after referee Slobodan Veselinovic had awarded Partizan a harsh-looking penalty which Zvonimir Vukic converted.
Vojvodina's incensed coach Zoran Milinkovic then led the players into the tunnel and also failed to turn up for his press conference.
His team also boycotted the presentation ceremony, leaving Partizan to celebrate in front of 10,000 of their fans who had packed the south tier of Red Star Belgrade's 55,000-seater stadium.
"We could feel it in the air right from the off that an incident of some sort was waiting to happen," Partizan coach Aleksander Stanojevic told a news conference after his team tried to persuade Vojvodina's players to finish the game.
"We were astonished Vojvodina were allowed to have the kickoff delayed by 30 minutes just because their fans were late and what they did at the end was a graceless act unworthy of a cup finalist.
"Still, we hope there air will be cleared before we play each other again next season because more tension of this kind is the last thing Serbian football needs."
Partizan goalkeeper Vladimir Stojkovic added: "They should never have been allowed to deliberate for 10 minutes whether they want to carry on playing or not, we were quite simply stunned by their behaviour.
The 27-year old Stojkovic, a former Red Star Belgrade player who became the first Serb to join bitter city foes Partizan in more than 20 years after he moved from Sporting Lisbon, was targeted by fanatical Red Star 'ultras' when Serbia played Italy away in a Euro 2012 qualifier last October.
"It leaves a bitter taste and of course we have mixed emotions about the way we won this trophy because we deserve better as a team which has carried Serbia's flag in Europe for some time now," he said.
"We were graceful in defeat after losing both league fixtures to Vojvodina but we can't say the same for them and we played no part in this scandalous finale."
