Congratulate the person who got the job you wanted. It’s hard, and that’s why it means something.

Wanting something and not getting it is a real loss, and there is no version of this where that part is not heavy. Congratulating the person who did get it does not mean pretending otherwise. It means holding two true things at once, that you are disappointed and that they did nothing wrong, which is harder than it sounds and is most of what makes it worth doing.

Send the short message when you can manage it. Take a day first if you need one. Then let yourself be properly annoyed somewhere private, because that is allowed too.