I want to reiterate something Susan K. said in her very good post. She asked that you take care not to call your girl a baby just now.
You are right to teach her to stick up for herself; however, please, please take greater care in the future with the words you choose to use to her. When she hears mom say "Everyone is going to think you're a baby," she thinks YOU are saying she's a baby (no matter whether she tells you "I know you're not saying it, mom" -- that's what she will hear in her head). When you tell her "They won't want to play with you," she hears, "They already don't want to play with you." She is sensitive, and yes, she does need to learn better ways to handle things, but what she hears from you right now is vitally important because your words matter infinitely more than these little tiffs she says are important enough to cry about.
Instead of "They'll say you're a baby and won't want to play with you," how about: "Other kids won't know what they have done that hurts you. They need to know or they may do it again. Talking and telling them 'Don't do that' is the only way you can stop it happening another time." Role-play with her the situations that made her upset and have her work on speaking up. Let her develop a "script" in her head to use the next time something happens. She will not do it perfectly and may forget to do it at all, certainly the first time there's another upset! But the point is starting the learning.
Since the teacher thinks your child is crying too often as well, ask the school guidance counselor to see your daughter, maybe for a couple of visits. Counselors are excellent at working with kids this age and giviing them very specific ideas of things to say and do in school situations.
Two other short things: Eight is a very, very typical age for sudden tears. My daughter would burst into tears at eight. All her friends, except a very few, were also very sensitive for a while at eight. This is typical for their emotional development at this stage and it does pass, but if she hears messages that are negative from you now, she will remember that long after the tearful eighth year is over.
Second: Ask the teacher if there is more going on than crying. Does your daughter slip away and basically hide (even in plain sight) when she is overwhelmed? Does she shut down, or alternatively, get excessively angry at others or even at herself, if things go wrong? Does she have great difficulty with changes or anything unexpected in her day? If those things are going on, she may need some professional help -- that was the case with a friend's dear child, who had issues that were beyond just normal eight-year-old sensitivity and who needed help that went beyond school counseling.