A million people, even a thousand people, is still a huge sample size when the average person maintains close relationships to... 5? and casual relationships to within 10-15?
"Im looking for 1 person. I don't really stay close to more than 5 people, but Im 'friends' with around 20 people. Who know around 20 people themselves. Who know around 20 people themselves. Who know..." etc etc.
The effect is cumulative. Winterstorm has the right idea, if you seem desperate or, god forbid, are people are going to notice that about you. It is not an attractive trait. Focus on your life and your wants/needs and eventually you'll find people who want to share time with you. If you're going into it with the mentality of "I want to have a relationship" then chances are you're failing right out the gate, because that almost never works (You probably wouldn't say yes to someone randomly walking up and going "Hey, I want to spend the rest of my life with you, you dig?").
The fact is that if you're lonely, you have to make something happen to change that. Break out of the routine, try something new, go out and make friends. If all you can think about is how badly you "need" a relationship, then you aren't ready for one. A relationship is a two way street, and if you're entering into one for selfish reasons, it's already going to fail.
So take it from someone who's made their fair share of mistake: Focus on making your life something people want to be a part of, rather than try and make someone a part of it. You'll find it becomes much much easier to meet people and * le gasp * get a relationship if you're out doing things, rather than wondering why you're single.