Dejan and his twin brother Darko began playing water polo in primary school, after a friend of their father's recommended that they tried it out. Both were attracted to other sports as well, but in the end decided to stick with water polo. At that time, Partizan had top level coaches who had emerged from the famous Yugoslav water polo school headed by Bata Vlaho Orlić (1934-2010). One of the top experts was Nikola Stamenić, who saw, early on, Dejan's potential as a player and even as a future coach. Dejan went on to play for Partizan with great success and became a member of the national team which he then captained for almost 15 years. On the other hand, Darko became the record holder for most games played in of the most successful national water polo teams of all time. While Darko ended his career as a player, Dejan decided to try himself as a coach.
Udovičić left the club on April 23, 2009, after his team's defeat against Jug in the Euroleague quarterfinals, which meant the Serbian champions failed to qualify for the Final Four.
At the first training session before the 2012 European Championship, Udovičić showed his players an image of the golden medals which were to be awarded to the winners of the Olympic tournament in London. He told his players, When you start feeling like training is taking a toll on you, these images should remind you to keep working as hard as you can!"[3]
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