First of all, we should note that it is very possible to argue this the other way. The Constitution sets up a government that is very much aimed at protecting life, liberty, and pursuit of happiness. It limits government, making it difficult for the government to violate these rights.
However, if you must argue that the Framers did violate the principles of the Declaration, you should look at the Declaration's idea that government should be by "the consent of the people." The Constitution does violate (one can argue) the principle of democracy. The Constitution does this by insulating the government from the people. It does not let the people vote directly for any part of government other than the House of Representatives. By doing this, it moves away from the more democratic vision of the Declaration of Independence.
(The Constitution also violates the idea that all men are equal, but it is clear that the people who signed the Declaration didn't really think people like African Americans were equal so we cannot really say that is a violation of the principles of the Declaration.)