I’m so sorry, OP! There will be more, and better, birthdays to come, but it’s shit that your partner ruined this one for you.
I assume there’s no actual bad behaviour from your family to him? Nobody was deliberately offensive or turning their back on him when he tried to engage? Unless he has some very genuine cause to complain, which it doesn’t sound like he does, he’s just having a sulk. I’ve had a couple of partners like this, when I was younger, (although neither of them behaved quite this badly). I wish I’d had more experience and had ended the relationships at once, because it was a big red flag that they were unable to manage their own emotions, unwilling to make compromises, and expected everyone else to cater to them and make them comfortable at all times.
Learning how to be a gracious participant in events where you know few people is part of being an adult. It can be a bit boring, and even a bit uncomfortable, but you suck it up for the sake of your partner. After the first couple of times things usually become easier; if they don’t, you discuss it, and come up with a strategy together.
Now, maybe you could have done more to include your partner and to make sure he wasn’t feeling left out? I don’t know - ask yourself whether that’s something to consider next time you introduce a partner to your family. But honestly, even if you weren’t as attentive as you could have been, his reaction was out of order. If he was uncomfortable he needed to use his words and tell you. He had the right to want to leave, but not to be sulky and mean about it. It was unkind and emotionally immature. In your place, I’d be reconsidering this relationship.