The Romanian coach handed in his resignation following his side's ninth-place finish at December's tournament in Hungary and Croatia.
He follows in the footsteps of Denmark's Jan Pytlick and Germany's Heine Jensen.
Romania will now seek to install a new coach to guide them through to the Women’s World Championship 2015 and beyond, with one eye on the Rio Olympic Games in 2016.
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Tadici's side finished one place better than two years previously, when they ended in 10th in Serbia, but one place off their goal of eighth in 2014. That proved the last straw for Tadici, who bemoaned his side's bad luck at the tournament.
"It was the best tournament for Romania in the last seven years," he said. "I think that we were even better than in 2007 when Romania finished fourth at the World Championships.
"If we had had Adriana Nechita [who was ruled out after the match against Denmark] for the entire tournament and if we had had a little luck, I think we would have been among the top four. And this would have been an amazing achievement."
Alexandru Dedu, the president of the Romanian Handball Federation, said: "It was a decision that surprised us, but he announced that he will be no longer the team’s coach. We will look at several candidates, but we will take our time."
Romania's next outing comes in June, when they face Serbia in a two-legged World Championship 2015 play-off. The second leg is scheduled to be played in Romania.
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