Single word to describe "make something worse"
Solution 1:
Similar in spelling, but more apt in meaning, to your example of exasperate is:
Exacerbate
Make (a problem, bad situation, or negative feeling) worse
Solution 2:
I think you are looking for Worsen
To make or become worse
or Aggravate
To make worse or more severe; intensify, as anything evil, disorderly, or troublesome