Before you deal with your relationship, you need to deal with yourself.
First, know that just because you've made a mistake, that doesn't make you a bad person, or even a bad father. We're all bad fathers in some ways... and good ones in others. The best we can do is try and learn from our mistakes, and build on our strengths. One of the best gifts we can give our kids is showing them how we recover from our failures and learn from them. When we model that, we teach them how to grow, too.
Second, you need to fully acknowledge the nature of what you did, and own it. Taking responsibility is the first step to growth. Again, I emphasise that your errors don't make you bad. They are just errors of judgement, and as such are an opportunity to grow.
Now, I don't know enough about your situation to be sure what happened, but it sounds like you made several mistakes:
(1) Kids break stuff; that's just part of the deal. (This is especially true of teens and near-teens. The stereotype of clumsy teenagers is accurate.) When a kid's body grows, it takes a while for their nervous system to readjust to their new dimensions, and they get clumsy. In addition, kids are also learning how to regulate emotions, deal with complex social demands, learn to take responsibility, deal with school pressures... its no wonder they make mistakes, sometimes. Even when they do their best to be careful, they break stuff. When we have kids, we just need to accept that, hard as it can be sometimes.
So, if the plate was that valuable, sentementally or otherwise, it should have been kept somewhere safe, and it it wasn't, that's on you, not your son. Alternatively, if it was just a regular plate, then it was just a plate. It isn't the end of the world that it got broken. Annoying, sure, but not the end of the world.
(2) You have made a plate more important than your relationship with your son.
(3) You need to understand that, for many kids, music is a significant part of their identity. As a result, the fact that this band isn't performing again isn't very different from him loosing a loved one. So, the pain he is feeling isn't just about missing a concert, but is also grief for the band itself. Your mistake was to deny him the opportunity to attend the band's "funeral" (last concert).
(4) You've accused and punished your son without good evidence, and that has damaged your trust relationship with your son.
What can you do?
Appologise. Don't just say sorry, but be specific about what you're appologising for.
Acknowledge your son's feelings. Name them, e.g. anger, loss. Show. That you want to understand him. Acknowledge that you don't understand how he feels, but demonstrate that you're trying to.
Tell your son what you plan to do differently in the future. Admit that you may make mistakes again, but that you'll do your best.
Admit that you can't "make up for" your son's loss, and explain that you want to learn how to be better in the future. Give examples, e.g. Find out the facts before making accusations. Be more ready to trust your son because he's a good kid.
Take an interest in your son's music. Listen to it. Find out about the band. Find out what people like about them. When your son is ready, talk to him about it. That will help him grieve, and also show that you're interested in him.
An idea: Have a plate made with the band's name and photo on it, and hang it on the wall somewhere as a gift to your son.
In all this, don't go overboard. Don't try to be "extra nice". The point is to show that you're learning from your mistakes, not grovelling.
Try not to beat yourself up. None of us is a perfect parent. I know I mess up all the time. But we're doing our best, and that's all our kids can ask of us.
