I accidentally caused my group partner to get a bad grade
How did you cause them to get a bad grade?
It was totally not my fault, I didn't have the chance to do my part on project
But you inferred it was your fault, and it's unfortunate you couldn't contribute enough. When you're working with a group it's best to prioritize them because everyone weighs equally here.
I don't have time to do everything!
No one is expecting you to do everything, just at least something. That's why it's call a "group" project.