"We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America."
If you are not a citizen, you are not a people thereof. You are here illegally and, according to that, excluded from it.
You should try reading past the Preamble, which merely states the purpose of the document.
Except there are plenty of people who are not citizens who are nevertheless here entirely legally.
The Fourteenth Amendment extends equal protection of the laws to everyone:
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; 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.
Note: this distinguishes between two classes of people. First, there are those "born or naturalized in the United States," who are citizens. No state may "abridge the privileges or immunities of citizens of the United States[.]" However, further, "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."
Generally, non-citizens lawfully present are entitled to the same due process, free speech, and other rights as citizens. They are not entitled to rights such as holding federal office, voting in elections where not specifically authorized, or whatever rights are covered by "privileges or immunities" but not by other provisions.
Non-citizens who are not present in the United States, or are unlawfully present, however, are not entitled to the same protections as those lawfully present. For example, discrimination on the basis of national origin would be unlawful against citizens. However, immigration authorities routinely do things like set quotas based on national origin.
Outside of the Bill of Rights, though, it doesn't make much sense to talk about whether the Constitution "applies" to noncitizens.
The bulk of the Constitution, Articles I-VII, entirely consist of outlining the roles of the branches of government, their powers, their relationship to each other, and the federal and state roles. The federal government is always constrained and limited to those powers actually enumerated in the Constitution, and does not gain extra powers depending on whom it is addressing.
However, the additional positive constraints of the Bill of Rights mostly, but not entirely, apply to non-citizens as well as citizens. The exceptions are few, and are those in which certain rights are expressly or impliedly extended to citizens, but not to people in general.
