"Americans" is how we think of ourselves.
OTOH, Mexicans regard themeslves as "Americans" and are somewhat offended by the American presumption that only people in the US are from the Americas...
You can't win this one...
Mexicans do not consider themselves as Americans. They consider themselves as Mexicans, as the constant boasting by the illegal Mexicans in America demonstrate. People in Canada, Mexico and in the other countries of Central and South America have no right to call themselves "Americans." Only citizens of the United States of America have the right to call themselves American as that is the name of their country and that is their nationality.
Now it true that Mexico is a nation that is part of the North American continent, but Mexicans do not consider themselves as part of the United States of America nor do they call themselves American (unless they are illegally residing in the USA and trying to scam the federal or a state government of benefits or to avoid deportation.)