European countries tend to dislike Americans because their image of the average American is a fat, lazy obnoxious and uneducated slob on welfare. A lot of countries think of us as power hungry and war-happy. The United States is the self-proclaimed greatest and most powerful country on Earth.
My sister went to France in January and when she came back, she said that the general perception of Americans in France is what is similar to what some Americans feel about Mexicans (which, by the way, is a perception I do not share), except that in France, Mexicans are more respected than Americans... most likely because of what I said in that last paragraph.
My sister's husband is Nigerian and so on the second half of the trip, she also went to Nigeria a few months ago to visit her his family. When she came back, she said that she felt horrible when she came home because we just have so many things that people in Africa would consider frivolous extras. They drive their cars into the ground because that's their way of life, and they're fine with that. Her exact words were "We just have so much... We don't even need this much stuff."
While she was still in Nigeria, she apparently fell in a ditch of some sort that was by the street, and when she did, almost everyone around her came to help and asked if she was okay, and NO ONE laughed. She said that she was really surprised by their reaction because, in America, bystanders would have laughed, stared, ignored her, or a combination of the three. They also thought she was rich because she was American.
As far as advice on how to handle it, really all you can do is try to understand why they feel the way they do about us. We complain about credit card debt and our our cars... Nigerians don't' have cars, and the taxis they do have have holes in the floors! Europeans are just tired of the ignorance.
Europeans are actually right about us as a country. We do take our freedom and our opportunities for granted, and we really as lazy, on the whole. A lot of us are lazy and obnoxious. Others who aren't lazy are power-hungry and greedy. The forefathers of our country have worked very hard to give us these rights, but in modern times, we really don't know how lucky we are. We just keep wanting more.