My mom died from cancer a couple years ago. I was at work the next day. I had to put it out of my mind while I was doing my job.
It's not a fun thing, and I don't mean this in a harsh way, but your parents did not raise you so you could give up when they were gone. You either die young, or you live to see those you care about die before you, and everyone on this planet has to suffer one of those things.
There is a feeling when you are young that "your world" is just going to be there, and it's there to take care of you. When you lose those people and those surroundings, it can feel like a wake up call. "What is left for me now," you might think?
The point is soldier on, be the best person you can be, be giving to those who need it, forgive those who have wronged you. This is the best way to honor your parents and show the world that they did good in raising you. "Admitting defeat" is giving up on life and that's not why they had you.
When you're out next, look around at all the people around you and realize that almost everyone that is of a middle to older age has gone through what you have. And even some younger people. Some people never knew their parents, or had really really bad ones. Be happy you were great friends with yours. Realize you're not alone in this experience. Spend some time with friends or other family. Maybe try to develop a new friendship.
I don't think there is really much anyone can say to change how you feel right now. But I would encourage you to struggle through these feelings, as it will definitely get better.