I don't do web development (but considering training to do some freelance) but yes that is the case, all these businesses wanting a site would opt to pay for cheaper services from Asia (quality is a different matter of course). I think one option is, aside from improving your portfolio, is to find a niche.
Web developers are asking for huge amount of money for tiny html/css edits. Their prices aren't fair and now they blame freelancers from all over the world because Indian guy charges 20$ instead of 600$ and they are bad, ruining their "profitable" business.
Do you ever take into account the cost of living in the respective countries? Web devs living in the US/EU ask for considerable amounts because that's the only way they can live in their society where cost of living is very high, this without taking in account the fact that when a dev charges 600$, he doesn't get 600$ in his pockets, there is taxes and a shitload of other expenses; ofcourse they are going to call devs from countries where cost of living is low "bad" because they are breaking the market by charging peanuts for their service...
The same can be said for any industry, for example customer service. Processes/services would either get outsourced or automated if possible coz that's what businesses do, cut costs. I understand that it sucks that devs in US/EU wouldn't be able to afford to live on the rate that Asians charge but that can't be helped.