Some Constitutional protections also apply to non-U.S. citizens.
First, it is true that some Constitutional provisions only apply to U.S. citizens. This includes the right to run for office, as well as protection from discrimination in the voting process.
Most other protections are extended to non-citizens. A lengthy discussion was published in the Thomas Jefferson Law Review, but really it's self-evident from the text of the Constitution. For example, first-amendment freedoms are really a prohibition for what Congress can do:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
There is no distinction between citizens and non-citizens; Congress just can't make these kinds of laws.
A second category of protections are ascribed to "the people" - a term which does not delineate between citizens and non-citizens. For example, the Second Amendment says:
A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
So the text of the Constitution specifies when citizenship matters. That the writers did not apply the concept of citizenship to all these other kinds of protections is evidence that it was not meant to be citizen-specific (according to the T.J. Law Review).
Most applicable to your example is this section of the 14th Amendment, which uses this same convention:
nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
Who Don't These Apply To?
These protections don't apply to everyone. For example, it would (obviously) be a mistake to think that the U.S. constitution protects Turkmeni protestors in Turkmenistan from action by their own government. Other cases may not be so clear. So where is the line drawn?
These protections apply to anyone subject to American law. This includes citizens, non-citizen residents, legal and illegal aliens, people living on military basis (whether U.S. citizens or not), and a host of other edge cases (such as foreign contractors who are subject to U.S. commercial law). However, it does not include people in other countries or who are otherwise not subject to U.S. law.