How to handle a student who will not accept that he is wrong?
Should I just tell him to talk to the instructor, and that my job is just marking?


Yes.  There's no point in getting into an extended argument with this student.  The student thought his answers were correct and you explained why they were not correct.  Since you've denied the student's appeal of the grade, the next appropriate step is generally for the student to appeal to the instructor.  

It's a good idea for you to warn the instructor that the student is likely to appeal the grade and to provide whatever information you can (such as a photocopy of the marked up exam question and any grading key that you used).