Dražen started playing for his first club, KK Šibenka, in 1976 as a 12-year old. At that time, the club played in the Yugoslav second division. Dražen was playing at all three club levels: cadet, junior and senior. Even in those early days he showed extraordinary leadership ability; he had some kind of power, and intellect to bring together senior players, who at that time may have been better than him. Dražen’s first coaches recognized this quality and saw in him a top player. They trusted him enough to let him play in the first division when he was only 15 years old. At first, he wore jersey number 9. From 1979 he wore number 4. At the cadet level he achieved his first national team success and with his home club, his first international success. At this time KK Šibenka was just starting; nobody expected success. Nevertheless, with Dražen European basketball came to Baldekin. Šibenka played in the finals of the Radivoj Korać Cup for two consecutive years, 1982 and 1983, both times against Limoges. Dražen did not like to lose. He showed his emotions on the court. A playful boy. During the game he would turn around, laugh, and push the ball through his legs. When he played against his brother, in a game between Šibenka and Cibona, Dražen left notes all around the house: “No entrance for Cibona players”, “No chance, forget taking points”.
In 1983, still not 18 years old, Dražen was Šibenka’s leading player and the key player in the finals of the national championship, the famous game between Šibenka and Bosna. Like many times before, and later, basketball came before anything else for Dražen that evening. For this game he missed his prom night but he won the national championship with Šibenka. Many people remember this game remains even today. Back then, few fans expected Šibenka, a club that had existed for only 10 years, to make it to the finals, let alone win the title. In the last two seconds of the game Bosna led 82-81. The referee then called a foul and awarded two free throws to Dražen. Coach Vlado Đurović told Dražen what he already knew very well, and which was so incredible – if he made both free throws, Šibenka would win the title. What a responsibility Dražen then assumed – to decide the championship at the age of 18. He made both free throws and Šibenka became the national champion of Yugoslavia. Unfortunately, the title stayed at Baldekin for only 16 hours because the national basketball federation annulled the result of the game because of some alleged irregularities. A new final was scheduled to be played on a neutral court in Novi Sad. Dražen said: “Whoever wants to go should go, I’m not going anywhere.” His teammates stood by him and refused to play a new game. That year, the title was taken away from them. KK Bosna was declared champion of Yugoslavia; Šibenka took second place. Nevertheless, Šibenka did not return the gold medal and today it sits in the museum next to many other trophies from the period when Dražen played for Šibenka.
While he was still playing for Šibenka, Dražen was one of the most sought after players in the region. Bosna, Zvezda, Partizan and many other clubs wanted him to play for them. He opted for Cibona, where he went after completing his military service in 1984. The decision was not an easy one to make, but Dražen said he just had to act on his basketball instinct. To achieve what he wanted in basketball, he had to go further. He played his last game in a Šibenka jersey in Omiš on 31 May 1984, after which four great seasons with Cibona followed.
- 1979, bronze medal at the Croatian Cadet Championship in Split
- 1980, gold medal at the Croatian Cadet Championship in Zadar
- 1981, silver medal at the Croatian Cadet Championship in Vogošća
- 1982, Radivoj Korać Cup Finals in Padua
- 1983, Radivoj Korać Cup Finals in Berlin
- 1983, Yugoslavian National Championship Finals