With world number two Djokovic resting in Serbia's skiing resort of Mount Kopaonik, the Swiss will be strong favourites to advance after former world number one Roger Federer joined Australian Open winner Stanislas Wawrinka as a surprise late inclusion.
"Novak is exhausted and made it clear he needs to recuperate for what will be a gruelling season on the ATP Tour," Obradovic told a news conference after the draw pitted Federer against world number 268 Ilija Bozoljac in Friday's opening singles rubber.
"He has played so many great matches for us, his priority this season is to recapture the number one spot on the ATP tour (from Rafa Nadal) and our fans need to understand that he is still a part of this team."
With Janko Tipsarevic sidelined with a long-term heel injury and Viktor Troicki suspended after missing a blood test last April, 2010 winners Serbia require what would amount to one of the biggest shocks in Davis Cup history to eliminate the Swiss.
Federer said he would have liked Djokovic to join the party but also made it clear Switzerland were looking forward to the prospect of taking full advantage of his absence.
"We were all hoping Djokovic would be here but we understand that he has good reasons not to be and we all know how much he has done for his country," said Federer, who often skips Davis Cup ties himself due to the competition's scheduling.
"It would have been more exciting and more difficult for us but what we have to do now is take this opportunity to try to win the tie."
Asked whether he plotted a late arrival in Serbia to outwit Djokovic, many of whose fans had hoped the world number two would have a last-minute change of heart and turn up to boost Serbia's chances, Federer said: "The press hypes a lot of things up because they want top players to hate each other, but my relationship with Novak is good.
"We've had a tough and fierce rivalry at times but away from the court we are friendly and do a lot of things together, like charity."
Wawrinka, who showed few signs of jet-lag and fatigue in Thursday's practice with Federer after a long-haul flight from Melbourne, was excited ahead of his clash with Dusan Lajovic on Friday.
"I feel great after winning a grand slam during two fantastic weeks in Australia," he said. "It's going to be tough to play straight after those exertions but I am enjoying the moment."
- Sports & Recreation
- Roger Federer