Do you need to use perspective in drawing anime/manga?

If you're drawing any kind of background, then yes it is necessary, otherwise your drawing will look out of proportion (unless you're just doodling). The lines are just guidelines btw. You can erase them after you've finished the drawing. Drawing a few guidelines isn't that complicated.

Anime Drawing Guidelines

One of the things about any kind of comic drawing (including anime/manga) is that the figures appear static if you do not have some kind of action in the frame, and the best way to show (and exaggerate) movement is by using foreshortening, and that can only work by using perspective.

You do not have to draw every single perspective guideline but you do need some idea of where your vanishing points are.

To be a better comic book artist just practice, practice, and practice. The majority of artists from Japan just keep on practice drawing by taking drawing classes, year in year out. I really hate them but they are good. Also a comic book artists artwork is there own. Not parts of other peoples work. You have to force yourself to be creative.