If your ex-girlfriend goes on thinking you're the asshole, frankly, she's probably better off. When a woman doesn't understand why her boyfriend leaves her, she gets incredibly clingy and makes the situation complicated. Then the inevitable long explanation comes and there is some closure on her part, but it really did nothing for you (especially when it doesn't result in your ultimate goal, which was to make her GO AWAY).

I'm not saying you have to manipulate the situation-- but if by some chance your girlfriend has reason to believe you dumped her for someone else, things are simpler and each person gets what he/she wants. She gets a sense of righteousness, and you get a hot piece of ass.