When you have the right mindset and approach, yes you can win back your ex.
But 95% of the freshly broken up couples miss the boat.
They do exactly what they should not do.
That's actually because you are in a state of emotional turmoil right after the break up.
You can win back your ex, if you follow these 3 steps.
Take a break: Yeah, you need a break after your break up.
Your break up being fresh, any decision you take regarding future of your life will be most probably wrong, mainly decisions regarding love and relationship, especially the actions you take towards getting back your ex.
Stop thinking about all those love and feelings now.
Calm down.
Divert your mind other things like hobbies, games, work, friends etc.
Seriously you need a break.
No ex for now: Most of the people think that the best way to get back with their ex is to call them up a numerous time and tell them "I miss you and I love you".
But this is the most ineffective way for you to win your ex back.
If you call them up and beg them to take you back, you are ultimately losing your dignity and self respect.
This will make you less valuable for them to take you back into their life.
Don't be desperate.
When you are desperate for something, it's for sure not going to happen the easy way.
The most important step: Now analyze all those reasons which caused your relationship to fail.
Start improving yourself in the areas where your ex expected improvement from you.
This is will impress your ex far more than calling them up and saying "I will change this time for good".
Change first, and you will automatically impress your ex.
After making sure that you have changed yourself completely and quit all those bad habits, you can call your ex now.
It should have taken some time for you to change yourself and you should have lost all those desperateness for him/her.
If you are still desperate or panic stricken, give some more time.
When calling back your ex, just start up like an old friend saying a hi and asking to hang out for a coffee.
Don't ever take this conversation into your relationship.
Talk about all those things in this world except your relationship.
Once you have built the trust and reputation for yourself as a good friend (that's your ex believes you are in no way going to offend him/her) you have bought yourself some time later to talk about your relationship and win back your ex.
The above given steps form the general framework of the answer for your question "Can I win my ex back?"