Your assumption is incorrect. The first reason why migrants don't bother with Slovakia is that it is much poorer than UK, GER etc. and therefore there are no
insane handouts waiting for them. Another reason is that for many of us (I happen to be a Slovakian, too) their culture is in absolute contrast with our culture and way of life. We don't see any point having our country saturated with the communities not willing to integrate (by this I mean respecting our law, culture and freedom). And last but not least - although sounding like an oxymoron, Slovakia has a large gypsy minority that many Slovaks see as a big problem, mainly because it is anti-social, messy and largely on the dole. So why would we want to have more "different" people coming to abuse the system, cause trouble or both?
As for Schengen, what's the point having it if we open the gates for uncontrollable mass migration? How do we manage to check all of those people potentially carrying various diseases or rule out they are not a security threat to us? We just don't and that's why the whole thing is wrong. The EU socialist establishment has completely failed (as socialists always do) to make sure our borders are safe and secure.
To sum it up - if Germany, Austria, Sweden etc. want tens of thousands immigrants coming to their countries it is their business. But do not force other countries to fulfill your stupid, out of thin air created quotas on immigrants thinking you have come up with some genius idea to sort out your mess.