Šajnović started to study music with eminent Yugoslav musicians - Emil Hajek (piano), Ljubica Marić (composing) and Mihajlo Vukdragović (conducting). In 1946, he went to Zagreb, in order to continue his musical training with famous conductor from Berlin - Fritz Zaun.
He graduated from the University of Zagreb Academy of Music, Croatia, SFRY, where he studied conducting, composition, and piano. While there, he studied with professors F. Zaun, S. Šulek and I. Maček.
Šajnović started his career in Zagreb Opera, as an accompanist. Later, he continued his engagement as an opera conductor and was finally appointed the director of Opera (1974-1979). After 37 years spent in Zagreb Opera, he went back to Belgrade, where was conductor and director of the Belgrade Philharmonic Orchestra (1984-1989) and Belgrade Opera (1993-1997).
Additionally, he performed and recorded as a guest conductor with many orchestras in Yugoslavia and abroad (Wien, Dublin, Mexico City, etc.) He was esteemed especially as the interpreter of the operas of Mozart, Beethoven, Verdi, Bizet, Wagner, R. Strauss, Smetana and Devčić. He also frequently performed compositions by Bruckner, Mahler, Reger and Shostakovitch.