They're not mistaken to be a bit worried, if a lot of their demand is from the US. To really start understanding these things... probably the best thing is to follow some good economics blogs.
Naturally, it get's harder for foreign countries to buy European goods, I understand that. It just seems as if the cause is too high a demand for European goods to begin with, so there is not really anything to worry about? At the moment the statistics are still good, apparently, as demand is still rising.
The other scenario might be that the markets are saturated, like, if Germany were to produce 10 billion cars per year, but there is only demand for 10 million cars. But then they could lower their prices or just produce less cars (thus saving costs), which would probably be equivalent to the Euro falling?
I think the problem is more that the dollar is falling than that the Euro has risen, and a lot of it has to do with money flowing around, debt, interest rates and lots of other things that I'll admit that I sort of grasp when I read them, but haven't digested well enough to explain them decently.
I guess if the rest of the world went broke, it would be bad news for export. Good products, but no buyers. But the exporting country would still have their presumably superior efficiency, so they can't be too bad off.