Losing someone that has played a significant role in your life is never an easy thing to go through. If you loved that person,then letting them go means saying goodbye to a special bond that you have. Even if you know that it is the right thing to do, it is natural for you to be sad. It is perfectly acceptable.
All breakups are hard. But that doesn't mean that you weren't right to end it.
Of course you're going to miss them. They were a huge part of your life for a long time. Of course you miss the closeness that you used to feel when you were with them. The bond between two people in love is a bond that you cannot find anywhere else.
But I am going to take a guess here and say that you haven't felt that closeness in quite awhile, even before the breakup.
Somewhere, somehow, your relationship changed. You stopped being happy. Maybe they started taking you for granted, maybe they got mean. Maybe they changed in some other way. Or, maybe you changed. And that is okay.
No matter what exactly happened, you made the choice to end the relationship for a good reason. You chose to look for happiness again, and that is important. It is important to remember that. You deserve to be happy and you're not getting happiness from this person anymore.
You must remember this when it starts to get hard, which is an inevitable event. When you start to miss them, you have to think about why it ended.
You made the brave choice to end something that no longer brings you happiness. It was hard, but you did it. Now you need to keep choosing your happiness over and over again until it no longer hurts. Because I promise you, one day it is no longer going to hurt when you see their name. It is no longer going to make you want to cry every time you see their face.
You will feel happy again. Very happy.
Time will heal, you just have to stay strong and continue to remind yourself of why the breakup happened.
You can do this. Be brave and be strong. Choose your happiness.