"Yeah, but the 14th Amendment (the Constitution) refers to US citizens."
It would be nice to think so, but the courts have ruled otherwise.
It's important to remember the circumstances of when this was written and why.
The amendment was written with the intention of protecting slaves or former slaves. There was a concern that some weren't citizens or could be railroaded in court using that arguement. Hence, they did not include the word citizen.
Interestingly, the 14th Amendment was used to legalize abortion, as well.
The 1973 USSC Roe v Wade decision specfically states that under the equal protection clause of 14th Amendment, the unborn child is not considered a "person" and therefore has no legal rights under US law (14th Excerpt: "All persons born or naturalized in the United States, and subject to the jurisdiction thereof......").
Roe v Wade author Justice Blackmun wrote that "the unborn have never been recognized in the law as persons in the whole sense" and are not entitled to constitutional protection until birth.