While most would see being sophisticated as a positive trait, Daisy diminishes the word's connotation. When Daisy scorns her own sophistication, she really means that she hates that she must live up to an image of sophistication. If she were not Old Money (or "sophisticated"), she would have been able to be with Gatsby when he returned from the war. If she were not sophisticated, she would not have to stay with Tom and endure the embarrassment of his countless affairs and injuries. If she were not sophisticated, she would have run off with Gatsby and the extravagant, New Money life he offered her. And finally, if she were not sophisticated, she would not run away from her problems and cover them up with her sophisticated Old Money.
Somewhere in the beginning of the book, daisy sobs while talking to Nick about how she hopes her child will be a girl and be a dumb and beautiful fool because thats the best thing a girl can be.