Bašić was one of the most prolific and versatile Croatian actors with a career that lasted for more than half a century. He first appeared on screen in the 1954 classic film Koncert. Through the decades, he played many different roles in many different films, often in international co-productions. He never became a star, but remained one of the most recognisable and dependable character actors. His specialty was playing the role of the suave aristocratic villain, especially in historic films dealing with World War II. He is perhaps best remembered for his role as "Mr. Fulir" in the 1970 cult musical comedy Tko pjeva zlo ne misli (One Song a Day Takes Mischief Away).