You can do this, but not in Edit Clause Mode, so you need to switch to Edit SQL Mode first using the toggle at top left.
As a test using ArcGIS Pro 2.2.4 I used the expression
NAME NOT LIKE '%ust%' to filter all countries except Australia and Austria from the Natural Earth countries successfully.
The warning (seen in the picture) that "The expression can't be edited in Clause mode" comes up if I try to toggle back to Edit Clause Mode using the blue icon at top left. Nevertheless, the expression can be used (just not edited in Clause mode).
If you take out the word NOT to make it
NAME LIKE '%ust%' then you can toggle back to Edit Clause Mode where you will see that the clause displays as
NAME contains the text ust.