Check again. Here are all of the continents in the world:
North America
Europe
South America
Antarctica
Asia
Australia
Africa
"America" is another way to say "The United States of America". That is why we are called "Americans", and Canadians and Mexicans are not (they are the other two countries located on the continent of North America). The name comes from when Christopher Columbus sailed across the ocean looking for India. He actually landed in America, which is why people still refer to Native Americans as "Indians". So, before they declared independence from England, the USA was just "America". After the Revolutionary War is when the name fully became "The United States of America".
Here is an excerpt from a website that details this:
"
How America finally came to be considered a New and Distinct Continent. But even after America was named, the idea that it was a distinct and separate division of the globe was not generally accepted. Some thought that South America was a great island or southern continent (like Australia); but the majority believed, with Columbus, that it was simply an immense peninsula projecting from southeastern Asia. People, indeed, spoke of the "New World," but all that they usually meant by that expression was newly discovered lands."
Leading Facts of American History