Well I am not expert on relationships for sure and spent most of my life more alone than 90% of people I have ever met I have had long spans in my life where I had no one. Not a single soul.
So I can really relate to people that go though this. But it really is not about the sex it is the lack of closeness with  you fellow humans that causes the melancholy. Intimacy opens us up and there is a sexual healing when you share yourself with another person that not only cares but loves you for exactly who and what you are. Society has created drones of preoccupied self interested people that rarely will make room for someone new.
Your depression causes a second problem namely depressed people are not attractive and do not attract people. So at the times you are in the most need you are also kind of set up to fail. Neediness is another problem it does not attract woman ether yet it is the natural progression for attention starved individuals. I am saying this from experience not judgment  cause I have been in the boat you are in except mine had more holes.
First thing is work on your self confidence self confidence is the 1# thing that attracts women.
Take more risks put your self out there more and stop taking rejection personalty maybe the person that rejected you was a train wreck
I tell you that I tried lots of things to Find that person then I just said Fuck it and surrendered and stopped looking and low and behold the universe brought me and my current wife together in circumstances so surreal so bizarre I could not ignore the attraction even in my jaded state. 
I can not give you help finding woman as that is not my strength for that I suggest you check out leo's videos. What I can do for you is teach you how to deal with loneliness until you do find someone. 
Fight depression by not doing what it wants. It wants you to stay home and feel sorry for yourself. It wants you to beat your self up and take rejection as a personal slight. I say Fuck that FIGHT MAN FIGHT.
Rule #1 activity defeats depression especially physical activity . Do not try to think your way out of a depression. Do not try to meditate away a depression. Fight your depression with physical activity. Get acquainted with a punching bag , start cycling . If you can find Groups to do things with you may even find someone with similar Interest  at the very least you could make a new friend.
Rule #2 meditation is for when you are feeling great after you beat the shit out of that punching bag and are no longer depressed Pick a type of meditation I would recommend moving meditation because it give you mind something to focus on.  Qigong tai chi or the eight step brigade or yoga would be great examples unlike sitting meditation like zan zen where those thoughts of loneliness will creep in.
Rule #3 learn something new read a book learn a new skill.
Rule #4 There are times when you depression is bad find a outlet write and try to process in some way  talk to someone or create something artistic that represents What you are feeling weather it be a poem or a piece of art. 
Positive affirmations sound silly but look yourself in the mirror in the morning and say "I accept myself for exactly who and what I am at this moment."
The goal here is not to just ignore your depression but to keep up the fight and process it and break bad habits that keep you locked in to this cycle as well as get your ass out of the house and doing some activity's where you can meet some people with the same interest as you.
On a last note I would suggest you you look into Taoist internal alchemy. You mine as well use all  that pent up sexual energy for something positive.
Taoist Yoga and Sexual Energy: Transforming Your Body, Mind, and Spirit Book by Eric Yudelove
The Taoist believe that internalizing your sexual energy and circulating it though you body helps cultivate a strong healthy immune system positive mental state as well as enlightenment. This is a lot more productive than masturbating. I have read many things on Taoist Internal alchemy 95% is completely useless to a westerner this would be the one and only book on the subject I would suggest to everyone. 
For actually the how to of meeting woman go to Leos videos I am still not Casanova just because the universe took pity on my soul.
Hope this helps Good luck