The best way to get revenge is actually by showing that you're not hurt anymore. You have to prove that you're fine now and that you've moved on, whether it's actually true or not. I'm sure your ex is already aware of the fact that you've been hurt, even if you've never said it to him yourself. Breakups always hurt, so unless your ex is an idiot, he would know that you're hurt.
That's why if you want to get back at him, you should act that the breakup and that your time with him wasn't significant to you. Just think about it: When your ex got a new partner, that probably made you feel a bit uncomfortable somehow (angry, sad, jealous, or whatever). That feeling goes two ways. No matter how hard your ex will try, deep down inside he will feel a bit peeved that he didn't deeply impact you.