First, I feel that this is a tragedy for everyone involved. To my knowledge, this is a universally bad situation.
Now, starting at a basic level, I have no problem with people leaving wartorn and ravaged countries and moving somewhere more peaceful. My ancestors did that when coming to the USA back in the 1800's, and they were perfectly justified. And Syria's five-way civil war is at least as terrible as what they had to deal with. Countries surrounding Syria have already absorbed a lot of the 4 million refugees. Lebanon and Jordan in particlar have accepted a huge number of refugees compared to their population. But even then, there simply are not that many places to run away to, so going to Europe is completely understandable.
From what I can understand, there may be over a million people who would want to resettle in Europe rather than sticking in Syria or the already overcrowded camps in the region. That is a lot, but I think Europe is big enough to absorb that. The European Union alone has half a billion people, a relatively wealthy economy, and good infrastructure. In the decade following 1900, the USA absorbed ten million immigrants, who not only didn't speak English but were largely from Eastern and Southern Europe instead of the earlier Western and Northern Europeans, and thus were fairly isolated. There were many problems involved, but the USA continued to thrive despite that.
My main worry for Europe would be that European countries have sometimes had trouble integrating immigrants. Immigrants don't necessarily need to shed their old identity, but need to be willing participants in their new country of residence. This involves knowing how to speak, read, and write the local language, following native laws that aren't life-threatening, associating with natives, and so on. In many cases, European countries have either not bothered or allowed migrants to create small colonies in a foreign country. That simply doesn't end well for either the refugees or the natives.