Pease don't worry. I was like you....always stressed about my shyness incase it affected my DDs but I've realised that kids make their friends in the playground and classroom without their parents present.
Playdates and all that do bring some together but real friendships are formed by the kids.
Having said that, it IS important for you to try...so that you get some support. I am SO shy it was massive effort when my DD began preschool and for literally a whole year, I felt like I was on the outside looking in.
What I did was volunteer to help whenever they needed someone....so if they have a fete or something, sign up t serve tea....it's a way of sharing experience with other Mums and often the ones who volunteer are also friendly.
Try to say hi to someone...a good way into a conversation is to ask a question related to an upcoming event at preschool "Oh hi...did you get that letter about dressing up on Friday? What are you sending yours as?"
That kind of thing....or simply "Hi...Tommy's mentioned Josh a lot...he really likes playing with him"
Parents LOVE it when you tell them their child is liked.
But above all please don't worry. Youre not the only one....playdates do get arranged but if you try to chat, you'll be able to ask someone for tea or a play aswell.