Teach my 4YO confidence

My daughter is 4 and attends pre-school half day. She is a happy, imaginative and active child at home, but not very open to people she doesn't know well (getting her to say Good Morning to strangers can be a struggle sometimes). Recently she came home from school telling me that the other kids from her 'girls group' don't want to play with her anymore. She repeats that for days now. She doesn't give a reason, just says they say 'no' when she asks to join a game or sit next to them etc. She then goes off and plays alone. I spoke to the teacher about it and she said that because my daughter is only half day and not full day, the other girls, who are mostly full day, bond deeper and I should consider sending her full day as well. I am trying to tell her that she should make new friends in class, that there are other kids she could play with but she doesn't want to. Either they are boys and play rough or they are too young, or they speak a different language or etc etc. When we are outside at a playground she rarely approaches any kids by herself and even is shy when we meet friends with kids she knows. I am wondering what I can do to make her stronger so she stands up for herself and makes new friends. Her personality is more shy and quiet - I am aware I cannot change that but what can I do to support her? (It might well be that this hurts me more than her)