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.

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).

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.

"[3] VK Partizan In 2011, Udovičić - with his fellow countrymen Vlade Divac and Slobodan Soro - appeared in a TV commercial for a Quit smoking campaign.