Not having friends does not mean that you are not worthy of having friends. It does not mean that you are not capable of having friends. You can be a kind, loving, friendly person and still not have friends. You can also be a pretty terrible person and have lots of friends. There is next to no connection between the quality of you and the number of friends you have.
There is definitely a lack of research on loneliness in psychology (what is out there refers to "social support" or lack thereof, and is a very messy topic) -- but there are some significant studies looking at loneliness and health outcomes, all pretty much saying that loneliness negatively impacts health. This is such a compelling and consistent line of research that the former surgeon general, Dr. Vivek Murthy, calls it an epidemic (scroll down on that one, also see this great interview about it).
His points are numerous and important.
His point on the stigma of loneliness is huge. We don't talk about it, and all too often we believe that if we did we would be judged for it -- that people would think that there's something wrong or that we would seem defective or unloveable. It's really a shame, because that is a complete lie.
As Dr. Murthy discusses in the article, our culture is task-oriented and doesn't provide many opportunities for genuine sharing and connection. Instead we have a culture of superficial sharing (i.e. Facebook), where it seems like other people are connecting, and we feel like we should be connecting, but the ratio of actual genuine connecting that is happening is minimal. We may even have lots of friends and maybe a partner, but for a range of reasons, but we might still feel lonely.
On top of that, as he mentions, people move around and change jobs a whole lot more than they used to, so there are many times we might find ourself "starting over." And having children? Yes, that too. Loneliness in these situations isn't a function of anything to do with you but rather the situation, and the seemingly endless time (years?) and effort it takes to build positive, mutually supportive relationships.
Add to that, people can be pretty risk averse. Making a friend can be risky. Maybe the person won't like you, maybe you won't like them, maybe it will be okay but totally draining and not mutual. Maybe you won't like their other friends. Maybe you will become friends and then they move again. (There's a This American Life bit that hits on the comedy that is making friends as an adult really well.) So, why bother?
Because then we end up lonely. We can end up depressed or anxious, and we may end up in co-dependent relationships, where we look to our partner (who we also likely didn't meet in real life) to fulfill our social needs. And, as the research cited above shows, our health suffers.
I don't say this to be the gloom and doom monster or make you feel worse, but I say it because loneliness is normal and shouldn't be stigmatized; it is temporary, and it is worth the risk to push through. Do what you love with or without people around (even the introverts), take some risks, allow people to support you, share bits of yourself gradually over time with people. Be patient, love yourself, and others will love you too.