"To someone's chagrin" means to their disappointment, irritation, or embarrassment, not sadness.
So it means she was irritated (she wanted you not to get the job) because I got the job.
"I'm chagrin because I couldn't do my job well" is not right, but you can simply change it to "I'm chagrined ...".
"chagrin" is both a noun and a verb ("It chagrined him that ..."), but not adjective as far as I know.