Is it an old proverb? Never heard of any culture that considered human beings to be made of stars. It is fascinating because now we know that we literally are made of stars.
I asked my mom (native Serbian speaker) and she said she's not heard of it as a proverb, and some Googling reveals that native Serbians are confused why foreigners seem to attribute it to us[1]. I also weirdly found a lot of questions on Quora and Yahoo answers asking for people to translate it to Serbian -- which explains why the proverb sounds slightly strange when read in Serbian. My guess is that this is actually some recent English proverb which someone decided to attribute to us (though it is neat that "zemlje" and "zvezda" do have a certain kind of rhyme).
Serbian here... Also never heard of it. But I suspect that it has something to do with another, similar one: U dobru se ne ponesi, u zlu ne ponizi/У добру се не понеси, у злу не понизи. Which roughly (because it is archaic) translates to: Be humble when all is good (in good fortune), do not submit to evil (bad, unfortunate, hard) times.