You don't need basic to understand ASM. However, you may want to know C to understand ASM.
btw, z80 ASM was really my first language. I did know ideas of program control and flow because I knew a bit of basic, but that's about it. Ideas about program flow and control. Because ASM can do things that the mind can not comprehend. There are some algorithms that ASM can do that you can't simply express in a higher language. That said, ASM is more powerful, but you can shoot yourself in the foot more easily than in C.
That's just my opinion of course. If you need help, just give a post.