The US most certainly did have national anthem at the time. What it didn't have was a Congressional proclamation stating that the Star Spangled Banner was the one and only official national anthem.
The anthem had been used in that capacity both at home and abroad since well before the Civil War. IIRC, the Navy made it official for it's use in the 1880s and the Presidency did the same just before WW1. The Congressional statement came about in the early 30s because of a Ripley's "Believe it or Not" column. Until then people had just assumed the anthem was the anthem and no official announcement was required.
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Bill
There were actually several songs used as 'national anthems' in the US, not just the Starspangled Banner. The following is from Wiki (ja, I know).
http://en.wikipedia.org/wiki/The_Star-Spangled_Banner said:"The Star-Spangled Banner" was recognized for official use by the Navy in 1889 and the President in 1916, and was made the national anthem by a congressional resolution on March 3, 1931 (46 Stat. 1508, codified at 36 U.S.C. § 301), which was signed by President Herbert Hoover.
Before 1931, other songs served as the hymns of American officialdom. "My Country, 'Tis of Thee", whose melody was derived from the British national anthem,[2] served as a de facto national anthem of the United States before the adoption of "The Star-Spangled Banner";[3] and "Hail, Columbia," served as the de facto national anthem from Washington's time and through the 18th and 19th centuries. Following the War of 1812 and subsequent American wars, other songs would emerge to compete for popularity at public events, among them "The Star-Spangled Banner".