What does her teacher say about what happens at school? I would work closely with the teacher. If you can take time off from work I'd also spend an hour or two observing in the classroom or on the playground. If friendships are as difficult as your daughter is portraying them the teacher will also be concerned.
Is it possible that your daughter is especially sensitive about being in a more structured and demanding classroom?
Does she need some help with learning some social skills that can be used in a structured group? Or perhaps she's still feeling insecure after making the change?
I think the first thing for you to do is to talk more with the teacher. If the school has a counseler talk with her/him. My granddaughter and a friend were having difficulties at school and the counselor formed a friendship group to help them learn ways to handle stress and be friends. This group happened because parents expressed their concerns to the counselor and teachers.
I would also give my daughter lots of positive support. In this case that means to sympathize with her feelings while encouraging her to try behaving in ways that will help her make friends. After talking with the teacher you'll know what to suggest for your daughter. It's important to not put down other kids or to agree with her when she says such things as "no one will play with me." You could say, "it sure does feel like no one will play with you." Keep in mind that your daughter is expressing how she feels. Her feelings may be related to events from the whole day but she may also be feeling that way as the result of one thing that happened that day.
After listening to and validating her feelings change directions and do something fun with her. Don't let the pity party go on for longer than 5-10 minutes.
Later, talk about friends in general in a casual way as you're doing something else. Talk about friends that she had in preschool and what they did to have fun. Relate that to school today. Use general terms. Ask about the kids in her class. Find out names. Ask what they look like. Ask what the kid is like. Try to make it a general conversation and not a "quiz" session. You may need to start out very slowly. When you talk about the kids in the class you are guiding her to realize that these are kids just like her in many respects. You are also helping her learn about an individual child's interests, abilities so that you can show her how she can get involved with this kid.
My granddaughter frequently cried when I picked her up after school in Kindergarten and first grade. My sense is that she had to hold in all the emotions that went thru her during the day. Once she was with me she felt safe enough to let them out.
Things happened during the day that upset her. Some kids, more than others, feel hurt when someone doesn't want to play with them right now. That same kid will want to play at another time but my granddaughter focused on this one event. She felt like this girl didn't like her and wouldn't ever play with her again. Drama begins early. It's not just teens who have it.
I do lunch playground duty once a week. I would see a child asking another child to play and that child say no. I realized that the reason the other child said no is that the asking child was asking her to play something different than what the group was already playing. When I see that I suggest to the "rejected" child that she ask to play with the other child or the group; to play whatever they're playing. That usually works.
Sometimes I notice a younger child standing alone looking wistfully at a group. I tell that child what the group is doing and suggest she join them. Just start out running with them. The kindergarten and 1st grade kids do a lot of chasing. Frequently one child will poke another child on the shoulder and say chase me. My granddaughter was sometimes disappointed because the other child said no. I suggested to her that she chase the one child instead of asking to be chased. She runs up to them and says, I'm chasing you. That usually works. If that child doesn't run, she tries another child.
Perhaps your daughter is shy and doesn't want to chase or be chased. I was like that at that age. The other activity this age likes is to play pretend. They pretend the play structure is a fire station and each kid declares his role as the play goes on. From there they act out a scenerio which they "define" as they go. There is rarely any discussion about what will happen or who does what. They just ad lib as they go. It appears that kids who don't start at the beginning get involved later by declaring that they are a certain character and joins the group. Sometimes kids drop out to do other things. The group is very loose in make up.
Every once in awhile I do see shy, withdrawn looking kids either playing by themselves or standing on the side lines. I try to be friendly with them and they usually withdraw. I don't know how to help them. Sometimes a teacher can get them playing.
My granddaughter is now in the third grade. Over the years I've seen all of her teachers and teachers on the playground help students get involved with others. A large part of teaching is teaching social skills. Skills seem to come naturally for some kids and are difficult for others. It seems to me that most of the ones that had difficulty are doing alright by the third grade.
Many children are quiet and followers. Sometimes they think that they should be different; perhaps be one of the social kids in the middle of everything. I think what helps is for every child to accept who they are and learn how to use their abilities without trying to be just like someone else. If that might be part of your daughter's unhappiness, help her accept that she doesn't have to be in the "social" group that seems to get all the attention. Leaders need followers.
Perhaps the group dynamics are different in Kindergarten than they were in Preschool. Perhaps your daughter was a leader and now isn't. Perhaps someone in preschool was a special friend whose friendship helped her feel more secure and she hasn't found someone special in this group. Even if there are some of the same kids in kindergarten that were in preschool the dynamics will be different.
Every child makes adjustments. It's possibble that your daughter is having difficulty making the adjustments. Some kids need more time when things change. And some need help finding their place in the group. Her teacher or the aide will help you find a way to help your daughter.
Since you work you may have difficulty getting to know her teacher. Most teachers will make an appointment with you after your work hours. Once you and the teacher know each other you can talk with each other by phone or e-mail. Do keep in mind that there are at least 25 kids in the classroom and some schools don't have teacher's aides. The teacher may not be able to spend as much time with you as you'd like or even need. Perhaps there is someone else who can help you. I've learned a lot from other parents. This group will help. However, a parent of a child in your daughter's classroom could be a great help. Especially so if they have older children and have been thru this before.
Your daughter will be fine. I remember being much like her in first grade. I was shy and sensitive; seldom played in groups. I frequently went home and cried. My mother listened to my concerns, reassured me that she loved me, held me and listened. She was also shy but she talked often with my teachers over the years and helped smooth the way when I didn't know what to do. She focused on me; not on "those kids" who I thought were mean. Over the years she repeated, "This too shall pass." I learned from her that even tho something feels tragic at the moment good times are ahead. As a result I became an outgoing adult. I've gained confidence over many years. Life is a process.