Nalbandis played in two of the three cup finals that Doxa reached during the 1950s and scored in one of them. He was also Captain of ΑΣΔΑΝ (The National Army Team). He was also a member of the National Football Team of Greece, but only played in a friendly game before immigrating to the United States. There, (like many international stars who immigrated to America) he continued his soccer career and played for Olympiakos Chicago.
It is worth noting that upon his return to Greece he had a very succesful coaching career.