Whenever a couple breaks up there's often one person who wants to keep the relationship alive...
So they call and text messages to their ex asking what happened, why they wanted to break up, how they'll change, and so on...
This will almost never work.
It comes off as needy and insecure and the other person usually winds up taking you for granted and leaving forever.
Instead of doing this you have to convey a much different personality; first by accepting the break up (I know it seems weird but this stuff works), and secondly by showing that you're a fun, confident person instead of saying it.
The majority of break ups happen because one person had an issue with insecurities, jealousy, or they just got boring.
Saying, "I'll change" isn't going to do anything, you're actually much better off if you show it in your attitude.
A good way to show is by first accepting what your ex has said, get on their side and say something like, "Yeah, this is definitely for the best, maybe down the line we can be friends".
You have to come off as if you really don't care what happens because you're just a positive person.
You can also convey a confident attitude by hanging out with mutual friends that you and your ex both have (make sure your ex isn't there) and just have fun without mentioning your ex at all...
If anyone brings it up say something like, "Yeah it was for the best, we both just need time apart".
It will most likely get back to your ex that you seemed really happy.