The action that you took sounds good. However, I'm wondering if your daughter got enough sympathy. Yes, she is over reacting. At the same time she does feel this deep pain. Over reaction and strong feelings are the norm at this age.
I have a tendency to react to emotional issues in an intellectual way. In this situation I'd tend to think and then say and/or show by my attitude that this is silly, especially if I'm tired.
I've been aware of my need to accept emotions instead of trying to "get rid" of them (especially my own) by being "practical" and dealing with the situation instead of the way I or anyone else involved is feeling. In the last few years I've learned a different way of handling emotional issues with my grandchildren. I tell them, "this is so sad that you've lost your bracelet." as I "sit" quietly with her for a few minutes and let her sob or tell me over and over what has happened. I'd only look for the bracelet if I wanted to do so. If I knew I'd be impatient I'd say "your teacher has looked and now we need to go home. Do you want me to hold you a little more in the car before we go home?"
I've often sat in the car holding my granddaughter while she calmed down. If she doesn't stop crying in a few minutes I divert her attention away from the "problem." What frequently worked for her is to say let's pretend. You drive. Where shall we go? As nearly as I can do so, my attitude is sympathy for her loss or whatever is causing her to feel such strong emotions followed by distracting her away from the pain and onto something pleasant. Isn't that how we "get over" our own pain so that we can continue with the day? Distraction.
By the time we get home she is usually calm. She may still talk about whatever had happened but she's dealt with the emotion and is able to then be more reasonable. I think that this works because I've acknowledged that her emotions are real and that I care about how she feels. She is able to feel the feelings and let go. When we don't acknowledge feelings no matter how "silly" they seem they remain locked inside of us. My focus is on her feelings; not on the cause for those feelings. This helps me to not think about how she is over reacting.
Of course I can't always do this. I have a time crunch. I'm too tired. I'm feeling cranky already. etc. But I work on showing my sympathy to the best that I can, given the circumstances at the time.
This usually helps with my granddaughter. Sometimes she isn't able to let go of how she feels. And that's OK. I give her a hug, if she'll allow it, and tell her we have to go home now. I say nothing while she cries. Crying is healthy. It is one way we let go of tension.
It doesn't usually work with my grandson. He usually expresses how he's feeling with anger. Trying to be sympathetic frequently causes him to be more angry. When I realize this I become matter of fact. I don't comment on the cause of his anger, even if I know it. I also don't tell him to stop crying if he's crying. I offer a hug. Sometimes that works. I allow him to have his feelings knowing he'll have to work thru them himself. (I suspect that his father tells him "big boys don't cry" or some such thing. He's trying to be a big boy.")
I believe that we can't teach anyone to not take things so hard. We learn thru experience that some things are more important than others. And we don't teach them by saying you're over reacting or don't be silly. We help them learn how to manage their emotions while they learn for themselves what is and is not important for them. At the time, the loss of that bracelet was very important for her. The feelings may have been caused by the actual loss or by what the loss represented. The actual loss wasn't important. How she felt about it was. Once we acknowledge the feelings and give her comfort she is more able to calm down. She probably doesn't know why she's so upset. I'm guessing it wasn't the bracelet since she didn't care that it was found.
I don't know if I've explained about feelings so that my thoughts can be understood. A brief summary might be that the feelings in most situations are more important than the situation itself. Once we've dealt with the feelings the solution is more easily found.