I think it is safe to say that, even though there was never a formal declaration of defeat, the United States lost the Vietnam War. The most obvious piece of evidence to this is that, in the face of mounting opposition to the war at home, the United States withdraw nearly all its military personnel in 1973 and South Vietnam fell to the NVA in 1975. The overall goal of the United States in this conflict was to prevent the spread of communism in Southeast Asia. The fact that the North and South of Vietnam were united under communist rule under the name Socialist Republic of Vietnam on July 2, 1976, should be evidence enough that the United States failed its mission.
The war was also lost in many ways at home. Back in the United States, popular opinion had turned against the country's intervention in overseas conflicts. By the late 1970s, US leaders found it nearly impossible to garner support for the use of American military forces overseas. President Ronald Reagan would call this the "Vietnam Syndrome." Many Americans in the decades after the war came to view the conflict in Vietnam as an unjust use of America's military and a monumental waste of human life. Since Vietnam, there has never been a serious consideration of reinstituting the draft. In short, the war was such a humiliation for America that it has effected foreign policy ever since. In all these ways, the Vietnam War can be considered a defeat for the United States.