To be honest I don't think anti-US sentiment or anything like that are the main reason. Remember the Xbox 360 sold decently well in Europe. If the Xbox was a good proposition, people in Europe would buy it.
The real reason honestly is probably going to be taste in games. Let's just think for a second about the main Xbox exclusive IPs, the 2 big ones are probably Halo and Gears of War. Xbox in general is the "shooters console", and most of its best exclusives are indeed FPS games. First person shooters are not exactly unpopular in Europe; I definitely know plenty of people who play shooter games. But they probably aren't as popular as in the US.
To continue the analogy to car brands, as someone who lives in Europe; some American brands do decently well in Europe; these being the ones that have a better product for the different needs of European customers. Ford in particular is a decently popular brand, it is not uncommon at all to find Ford vehicles. The Ford Transit regularly appears on "best selling vans" lists here in Spain. And the Ford Fiesta is also a decently popular car. However, a vehicle like the Ford F series (huge pickup trucks) would never sell in Europe despite being the best selling car in the US. Ford seems to have done well and sold small vehicles (and vans) in Europe, and pickup trucks in the US.
If Microsoft offered a product that had exclusives and an image better oriented towards the tastes of Europeans, more Europeans would buy it.
The reason is interestingly not that different from the reason why Xbox sells horribly in Japan, except toned down by a lot (European sales figures are still way better than Japanese ones for Xbox).