My son wanted to sit with me and watch his own pre-school graduation. I got him to stand on stage with his class but he cried through the whole ceremony.
He often played "around" other children in new situations and was slow to participate in new situations - requesting to go home, or just obviously being uncomfortable.
He has no siblings, but played well with the neighbor children, school mates, and family friends. He just wasn't good with first meetings of new children in new social situations.
You know what, he outgrew it. He did scouting in 1st and 2nd grade, and began team sports in grade 3. He "grew" into it.
He is 15 now and has a small group of close friends, and a larger group of school/band friends. He has online friends, friends that are girls, ones that are boys, and gets along well with adults and other children and teens.
Three years old is very young - not all toddlers are precocious. Give your son time to grow and mature. Realize that he is his own person and just because you want him to be a social butterfly does not mean he is ready to be one. Also, is he closer to 2, or to 4? That makes a difference. A young three year old is at a different level than an "old" 3 year old.
Instead of forcing him to play soccer right away, maybe take him just to watch - let him see the other kids playing and interacting. Let him learn by watching them. Once he becomes familiar with them, in that passive way, he may be willing to go onto the field and play with them.
Give him time. This is the advice that my family and pediatricians gave me. They were right. My boy grew up just fine.
Good Luck
God Bless