Actually Americans refers to people from the United States. Sure America is 2 continents, but that is just how it came out. There is not any other alternative to "American" besides "person from the US" which is too long to write.
You could say "Columbian," "Fredonian," "Usonian," "Washingtonian," or others proposed by Henry Mencken, or even "Yankee," which just about everbody knows to be associated with people of the United States of America.