You know when someone tells you something you don’t like but it’s true and you just have to accept so you make a face like this :| widening the mouth and making dimples in each end and perhaps shrugging Would you call that a smirk? “When i ask her if that was true she ___”
I would not denote that situation as a smirk. Typically smirking faces are a smug form of smile, which is usually to demonstrate a gained pleasure in someone else's pain https://www.vocabulary.com/dictionary/smirk
I believe you are referring to a grimace, where your face contorts in a manner that expresses disapproval http://www.dictionary.com/browse/grimace
A smirk is a smug, conceited, or silly smile. So I suppose if what someone says makes you feel a bit silly or stupid, and your reaction is to make a silly smile, then yes it could be described as a smirk.
The body language of such as a smirk might convey a different message however, perhaps one of sarcasm or annoyance. So, be careful who you smirk at! Do it too often and you might be perceived as childish or peevish.