A fellow writer asks: "How do I get motivation to keep writing something that I know is crap?"
My answer: Modify it until it's not crap.
If you are working on a project that you have control over, then take control of it. If something is screaming at you that it's crap, then some part of your project may be actively awful. If that's the case, then change that aspect until it's not awful anymore.
Suppose you're writing a story about an elephant that is the size of a squirrel who goes on adventures in a city park, but it just feels like crap to you. The first step is to isolate the problem. Is it this character that you think is crappy? Is a squirrel-sized elephant just too silly or ridiculous to get into? Or is the problem the story itself? Is a generic adventure story too plain and uninteresting?
If the character is the problem, then change it. Make it be something other than an elephant (maybe a sheep or a giraffe). Or, keep it as an elephant, but make it be the size of a dog instead of a squirrel.
If the story is the problem, then change it. Instead of it being a playful adventure, make it be a quiet introspection of being such a unique and bizarre creature. Make it be a lamentation of being the puniest version of a creature known for its enormous stature.
As I said in my original response, you are feeling conflicted. Some part of you still believes in the project, but some part of you is disgusted. If you simply change the disgusting portion into a more palatable form, then you'll be good to go.
As always, it is far easier said than done. I won't deny that. But I will tell you that if you start thinking about and playing with your stories, you can make these modifications a lot faster than if you just sit around in woe.