"My score was not good, but I passed."
Translation:점수가 좋지 않지만 통과했습니다.
Also, I don't think 통과 is a good word to use here. 합격 would probably be more appropriate given that 통과 has more of a feeling of passing something into existence or gaining entrance into some area or some idea.
For instance 통과: The law was passed; I passed through the gate
And 합격: Passing a test; passing an audition