Λίγο is not followed by genitive. Without the definite article it is followed by accusative and with the definite article is followed by απο+accusative. So, θέλω λίγο κρασί=I want a bit of wine, Θέλω λίγο από το ψωμί=I want a little of the bread.

That's exactly what I tried, even though I knew, as I was typing, that it was incorrect. It was all I could think of, and had to try something