The Paris, Texas school district was forced to apologise on Tuesday after the performance at Hillcrest High School was greeted by heavy boos and several objects were hurled at the band.
Charles Grissom, the band director, said the song and flag were part of a musical performance called Visions of World War Two.
It was performed at the high school in Dallas on Friday, which was also Rosh Hashana, the start of the Jewish new year and one of the holiest days in the Jewish calendar.
"The performance is an attempt to factually portray the history of World War Two, triumph of good over evil, and to honour our veterans for their sacrifices in ensuring freedom throughout the world," Grissom said in a statement.
He added later he made a major mistake in judgment.
The show included the flags of other nations fighting in World War Two, such as France, Britain, the United States and Japan.
The flags were waved twice as a musical selection from each country was played.
"We regret there was a misunderstanding. We strive to be sensitive to the feelings of others and are always willing to amend our actions when we fall short," said Paul Trull, superintendant of Dallas schools.
The band will still perform the musical composition, but it will only have the United States flag on display, he added.