Using HSBC's teller (Counter Service Officer) as an example, HSBC only requires that candidates must pass HKDSE for Chinese, English and Mathematics. So as soon as you did not fail any of the above subjects, you are still fine.
Even you fail any of the above subjects, you can still enroll into Yi Jin Diploma to repair your defects in HKDSE.
It is true that banks prefer candidates holding higher qualifications. However, it does not mean your chance is smaller than those having higher qualifications. Other factors, such as your assessment test score (if any), help making a difference as well.