Have you ever taken a look at a first draft of a story and said "What a piece of crap?" It happens to me all the time. It's really quite depressing when you read through the story and think "This is nothing like what I was trying to go for" or "There's so many errors and mistakes I'll never get it to turn out the way it needs to." When coming to these types of low points in writing, it is important to remember that it's all part of the writing process. First drafts are suppose to be crappy. The most important thing is getting the story on paper anyway that you can. Once it's there then it will be possible to go back and make changes.
One thing I always do when completing a first draft is to send it to a few of my writing colleagues to critique. I then let it sit and stew for a bit. If an idea or thought pops up about the story, I write it down in a notebook for review later. After enough time has gone by (about a week or so), I sit down with my notes, with any critiques I've gotten back, and work through the crap. I usually end up with a fairly decent second draft, which makes the whole writing thing feel like it isn't such a downer after all.
I recently stumbled across a few other blog posts about the first draft. One from A Place For Writers called Is Your First Draft Really Awful? talks about the importance of writing the first draft, the time it takes and understanding that it is a process. Also check out The Blood-Red Pencil's blog Shitty First Drafts as Maryann Miller talks about using the first draft as a playground for writers and getting the story down with the "inner editor" turned off.
Don't judge the quality of your writing by your first drafts, use your finished pieces for that. The process is there for a reason. It helps workout all the stuff that doesn't, so that you're free to discover the stuff that does. It' about getting the beginning, middle and end down so that later you can fix and polish it up. Accept the first draft for what it is and move on. First drafts are a necessary evil.