Tadic said on Monday: "Undoubtedly, Milosevic had demanded a higher level of health care. That right should have been granted to all war crimes defendants."
Milosevic, the former Serbian president, died on Saturday of a heart attack in his prison cell near the tribunal in The Hague, Netherlands. He had recently demanded to be temporarily released to go to Moscow for treatment after years of suffering from heart problems and high blood pressure.
But the judges refused, ruling that even with Russian guarantees to send him back to the court, they were afraid he would not return.
"Unfortunately, today we are getting messages from the tribunal that they are not responsible," Tadic said. "I think they are responsible for what happened."
Tadic, whose Democratic Party led a popular revolt that toppled Milosevic in 2000, said that despite "the lack of credibility" the tribunal has among Serbs, Serbia will try and hand over more war crimes suspects, including top fugitive Ratko Mladic.
Milosevic's death "won't jeopardise our cooperation with the tribunal".
Lavrov said Russia did not fully
trust Milosevic's autopsy
In Moscow, Foreign Minister Sergey Lavrov said Russia did not fully trust the autopsy on Slobodan Milosevic and wanted to send its own doctors to examine the body.
Milosevic's son, meanwhile, said the family would consider asking for Milosevic to be interred temporarily in Moscow until a funeral could be held in Belgrade.
Lavrov also repeated Russia's criticism of the UN war crimes tribunal for refusing last month to allow the former Yugoslav president to travel to Moscow for medical treatment.
Clearly stung by the rejection of Russia's "100% state guarantee" that Milosevic would return to finish his trial following treatment, Lavrov told reporters that Moscow was "disturbed" by the decision.
"It cannot fail to alarm us that Milosevic died shortly afterward," he pointedly added.
Lavrov said: "Essentially, they didn't believe Russia. In a situation where we weren't believed, we also have the right not to believe and not to trust those who are conducting this autopsy."
Russia has asked the court to allow its experts to "take part in the autopsy or at least acquaint themselves with its results," Lavrov said, adding that a team of medics was ready to fly "urgently" to The Hague.
The Interfax news agency quoted an unnamed Health Ministry official as saying a Russian team would leave for the Netherlands early on Tuesday.
"Essentially, they didn't believe Russia"
Russian Foreign Minister
Milosevic's body will be claimed by his son, Marko, on Monday or Tuesday, Milosevic's lawyer, Zdenko Tomanovic, said.
Although authorities in Belgrade had issued an international arrest warrant for Marko Milosevic in 2003 for alleged abuse of power, the charges were later dropped.
Speaking in an interview with Russian state-run television, Marko Milosevic said he would appeal to authorities to consider allowing Milosevic to be interred in Moscow temporarily.