Time. Time. And more time. He only just turned three; he's still barely out of babyhood, really, in the big scheme of things. It's great that he is in a preschool setting; that will be a huge help to him figuriing out how to get to know and how to play with other kids. I bet if you were watching other kids in the preschool as closely as you are watching your own you would notice that other kids have their own individual issues with things like starting conversations with "I have black shoes" or "I hate blueberries" or "I ate oatmeal today." You'd find that other kids who seem very confident with some playmates might suddenly seem shy or awkward with other playmates. So take a deep breath, remember that he's only barely three, and relax a bit. You will find playdate friends soon enough if you talk with other preschool parents. You're doing plenty to help him learn social skills. It is VERY typical for a child his age to behave exactly as you describe.
He may seem to you to be "sad" about not having friends, but remember -- that may to some degree be your adult mind placing adult ideas on his behaviors and moods. Sure, he wants to play with someone, but right now he wants you more than anyone. Yes, he may say that he wants to play with another kid this instant, but in fifteen minutes he likely will be happily engaged doing something else. He is not suffering because he's an only child, by the way; only children don't have to have siblings to be socialized or learn how to play with other kids (I know plenty of siblings who don't get along with each other and who teach each other nothing about socialization!).
He's fine. You're doing fine. Give him time. That's hard to hear when it seems like other kids are little social mavens, flitting from friend to friend with ease, but believe me, their parents could certainly tell you stories about those kids' own social quirks, issues or concerns. It will all smooth out eventually. If you continue to worry, talk to the preschool teacher or director for a reality check; she or he likely can tell you how your son is doing, based on the teacher's more objective experience with many kids.
One other thing: Once he is in a preschool that is not "mommy and me" he may change somewhat. Kids often behave quite differently in a setting where there isn't a parent present. For now the preschool sounds wonderful and is a great transition for him, and your being there is just right. But eventually he'll be in a preschool where you're not there (correct?) and that will push him further along socially -- when he's ready for that.