First of all, Europe has been a part of the problems that have driven refugees there in the first place. It was primarily Europe and America that instituted the modern international system. Insofar as the UN has been unwilling or unable to deal with the crises in Syria, Europe is in part to blame. ISIS was created in part because of the inability of some European countries to stop the US-led invasion of Iraq and the active participation of other countries, and in part because of other factors that stem back through globalization, colonialism, etc. European-owned firms did business in the region.
Every time these debates come up, people try to pretend that these refugees are aliens from another world, that it's just some coincidence that they're over there and the host country is over here. It's almost always false. We're all interconnected. We live in a world where people have trade, political and social connections. Why does that conveniently end when it comes time for humanitarian aid?
Second of all, we are responsible for the predictable consequences of our actions. If Europeans do not take in these migrants, many will have to go find somewhere else to live. That will necessitate the loss of additional resources, time in the marketplace, and will even cause deaths.
If Europe can take them in, they have a moral responsibility to do so. If we were talking about a medieval society that already had its own serious problems and could barely feed its own people, that'd be at least debatable. But here, Europeans could easily accommodate Syrian refugees.
We used to have a belief in hospitality, in xenia as the Greeks called it, that no traveler should go without a safe port. That idea remains just as valid and as noble now as it ever was. And it's even more important.