Don't worry too much. I know when I was starting out with anime drawings, mine didn't look too anime-styled... they actually looked closer to Bratz dolls.
Then I gradually shifted my art into more anime style, though it still looked like elementary school style anime drawings. I would draw regularly before bed, and each time I drew I noticed I would get a little better. I also would observe the art styles of different series, and learn how to differentiate "anime" style and "western" style.

For the longest time, I could only successfully draw chibi characters, but eventually would practice a lot with standard scale characters until I got better. It's important to take constructive criticism and learn from what professionals tell you.

I believe the hardest part of drawing anime, is the cheek/face shape. It's something I still have trouble with sometimes, and takes a billion ctrl+alt+Z for me to get it right(in Photoshop).

One of the most important things of all... don't force yourself. This should be a hobby, and not slave labor. Only do it when you feel like doing it. You won't really get much worse than you currently are.
I rarely ever feel like drawing myself, but even with year-long gaps between drawings, I seem to get better each time.