[2] Džajić is widely considered to be one of the best footballers to emerge from the former Yugoslavia, and one of the greatest left wingers of all time.

[3][4] Džajić was known for his crosses, passes, dribbling with great pace, natural technique and his left footed free kicks.

A left winger, his career with the club spanned 590 games and 287 goals by winning five league titles and four Yugoslavian Cups.

Though only 17 years and 8 days of age, Džajić was handed his first team debut by head coach Miša Pavić in a Yugoslav First League match against FK Budućnost Titograd on 8 June 1963, which finished 0–0.

[6] The match was played at Omladinski Stadium at Karaburma because Red Star's famous home Marakana was in the final construction stages.

An expert dribbler, his left foot provided a constant stream of goals for teammate Vojin Lazarević.

He played in the 1968 European Championship semi-final against England, in which his 87th-minute lob over the goalkeeper Gordon Banks gave Yugoslavia a 1–0 victory against the then world champions.

It's true that our failure in the final hurts me, but from today's perspective, I can say that we made a great result.

He played in Yugoslavia's opening championship game draw with world champions Brazil and scored one goal in a record victory of 9–0 against Zaire.

On 16 November 2012, Tomislav Nikolić, the President of Serbia, signed an exempt from criminal liability of all charges.

[15][16] On 2 December 2022, Red Star Belgrade announced that the number 11 worn by Džajić will be retired from the 2023–24 season on.