How does the teacher handle things in the classroom? Does she have a daily "helper" to help her with classroom duties? My kids LOVE the days that they are "the one". It makes them feel so important.
You might try telling your daughter how to start a conversation with some of the other girls. "Hi, my name is Sally. What's yours?" Or whatever you choose. You might even role play with her some at home so she will feel comfortable in starting a conversation with these other children. Or go out to Chuck E Cheese (or even McDonald's) and encourage your daughter to approach one of the other children and ask if they want to play.
I agree with the teachers, it will just take a little time. But I also think it is part of their job to "assist" with the transition, if you will. If she is so lonely on the playground, they should also gently encourage her to play, and encourage the other children to let her join the "group".
Good luck to you. I know it is painful to watch your child try to transition to the growing up stages of life. Just remember, you were in her shoes once, and you turned out just fine.