Largely true. However, the Constitution does have a statement of purpose, one which reflects the moral principles of our charter:
"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."
Sure ... but it's not the focus of the thing, and the authors wisely kept it very brief. I see it not so much a justification, as a reference to the justification in the DoI. They met to "alter or abolish" the form of government established in the Articles of Confederation, and "institute a new government". I think the phrase "more perfect Union" tells us a lot about their thinking. A less perfect union already existed; their purpose was to improve on it. The focus is on outlining what the "new form of government" would look like.
daisy mae of the usa has raised an interesting point regarding the DOI and the US Constitution's lack of specific wording such as that contained in the Declaration.
One document which is available to us today and which traces the happenings of the founding period is John Quincy Adams' New York City speech, "The Jubilee of the Constitution. . . ," delivered on April 30, 1839, at the invitation of the New York Historical Society. In it, he traces the ideas and the history of the Constitution, pointing out that the Articles of Confederation were inadequate for accomplishing the great philosophy of the Declaration, but outlining why the 1787 Constitution did. It is available here.
This man, whose father was instrumental in getting the Declaration adopted when JQA was only 9 years old, served in numerous capacities in the new government, including as President. His historical record should be one that is consulted frequently as an authentic statement of the meaning of our documents.
In one portion of this lengthy history, Adams states:
"But this institution was republican, and even democratic. And here not to be misunderstood, I mean by democratic, a government, the administration of which must always be rendered comfortable to that predominating public opinion, which even in the ages of heathen antiquity, was denominated the queen of the world: and by republican I mean a government reposing, not upon the virtues or the powers of any one man - not upon that honor, which Montesquieu lays down as the fundamental principle of monarchy - far less upon that fear which he pronounces the basis of despotism; but upon that virtue which he, a noble of aristocratic peerage, and the subject of an absolute monarch, boldly proclaims as a fundamental principle of republican government. The Constitution of the United States was republican and democratic - but the experience of all former ages had shown that of all human governments, democracy was the most unstable, fluctuating and short-lived; and it was obvious that if virtue - the virtue of the people, was the foundation of republican government, the stability and duration of the government must depend upon the stability and duration of the virtue by which it is sustained.
"Now the virtue which had been infused into the Constitution of the United States, and was to give to its vital existence, the stability and duration to which it was destined, was no other than the concretion of those abstract principles which had been first proclaimed in the Declaration of Independence - namely, the self-evident truths of the natural and unalienable rights of man, of the indefeasible constituent and dissolvent sovereignty of the people, always subordinate to a rule of right and wrong, and always responsible to the Supreme Ruler of the universe for the rightful exercise of that sovereign, constituent, and dissolvent power.
"This was the platform upon which the Constitution of the United States had been erected. Its VIRTUES, its republican character, consisted in its conformity to the principles proclaimed in the Declaration of Independence, and as its administration must necessarily be always pliable to the fluctuating varieties of public opinion; its stability and duration by a Re overruling and irresistible necessity, was to depend upon the stability and duration in the hearts and minds of the people of that virtue, or in other words, of those principles, proclaimed in the Declaration of Independence, and embodied in the Constitution of the United States."
Another history of the ideas underlying American's founding may be found at this web site, at which Richard Frothingham's outstanding 1872 "History of the Rise of the Republic of the United States" can be read on line.
This 600+-page history traces the ideas which gave birth to the American founding. Throughout, Richard Frothingham, the historian, develops the idea that it is "the Christian idea of man" which allowed the philosophy underlying the Declaration of Independence and Constitution to become a reality--an idea which recognizes the individual and the Source of his/her "Creator"-endowed life, liberty and law.
Although "daisy mae's" question is not fully answered within these two documents, they do address some of the underlying issues implied in the question.