firstly, No offense ... we all experience these things, especially during the initial days here. but you have shown too much weakness when you cried. hope the nasty ppl will never see tears again on your face.
It's important to reach out and experience different ppl, understand their behaviors and mindsets. It's painful but necessary to have negative experiences like this. Think about it. What will you do the next time you face this? I don't think you will cry again. And the third time? You will probably not bother at all, coz you understand that even in Singapore, you still have a lot of exciting things to do, many interesting friends to know.
It's true that many ppl are resentful towards us scholars. If you go abroad, ppl will complain that you are taking their advantages (though it's a valid complain if you don't pay off) If you work hard here and do well, some losers will say you take their opportunities. Coz in their minds, you should always be the inferior "cheap labors". Of coz if you do badly, you are a live example of the government's failed investment.
Having said that, most local ppl will not be foolish enough to take the resentment down to personal level, except the ones you encountered. (they are apparently the less educated group of the society) Most of the time, it's just like what happens between us and the japanese -- we can get angry talking about japanese as a nation, yet we can have good Japanese friends.
The point is, the high-level resentment will not really affect your work and social life. Even if you are not keen about mixing around with locals, Singapore is a highly international country and there are so many expatriates like you. If you don't want to work for local companies, there are abundant MNCs too. So, it's up to you to choose. Reach out, and be happy.