Vladimir Putin in his September 12 op-ed in the New York Times:

"I carefully studied his [Obama's] address to the nation on Tuesday. And I would rather disagree with a case he made on American exceptionalism, stating that the United States' policy is 'what makes America different. It's what makes us exceptional.' It is extremely dangerous to encourage people to see themselves as exceptional, whatever the motivation. There are big countries and small countries, rich and poor, those with long democratic traditions and those still finding their way to democracy. Their policies differ, too. We are all different, but when we ask for the Lord's blessings, we must not forget that God created us equal."

American exceptionalism is not an attitude of self-congratulation or of superiority of Americans as individuals.  Rather it is standing in awe of the great edifice created by the Founding Fathers, expressed in the Declaration of Independence and vouchsafed in the Constitution.

The Founding Fathers were heirs of the Scottish Enlightenment, which held that the individual was sovereign and that "governments are instituted among men (meaning mankind), deriving their just powers from the consent of the governed" (Thomas Jefferson in the Declaration of Independence).

As compared to what?  As compared to the 5,000 years of recorded history where, with very few exceptions - the Greek city-states, the Roman Republic - the individual is/was the chattel of the sovereign or, as in the French Enlightenment, the citizen was created by the State and is its servitor.

The glory of America is what ordinary people can accomplish when accorded their dignity as individuals under liberty and Judeo-Christian morality.  That is what is meant by "American exceptionalism" not that Americans are somehow more worthy than people of other countries.  America is more worthy, America is exceptional, because it is the manifestation of the climax of Western philosophy and tradition, respecting, indeed built upon individuals by recognizing their God-given rights.