I think it's okay, at 13, to let kids start to figure things out a bit on their own. This is a recent injury, and it's tough to deal with all the adjustments. My son was a XC runner and I know how devastated he was when he got mono during his senior year. It took him a bit - and he was looking at not getting college applications in because he was too exhausted to complete them, the essays, etc. There could have been huge repercussions.
Your son may also be a little embarrassed. I know, and you know, that runners fall all the time and it's not a sign that they aren't athletic. I've seen kids get sick too, when they don't yet know what they can eat before a meet. It's something they have to get used to. And he's probably in pain a bit too. It's hard to shower, to sleep, and more.
And don't forget that teen hormones are kicking in, and that moodiness is likely going to be a part of your family for a few years!
So I don't think you have to buy into it in the sense of sitting with him and participating in the misery, but you can let him deal with it. Disappointments happen, not everything in life works out great, he's going to have off days as a runner, a student and a human. They don't define us - and he needs to learn that. Let him know you have confidence in him and his ability to figure it out and get used to things. You can encourage him to talk to his coach and see what sort of a workout program he can do in the meantime. For example, he might be able to safely do leg presses and stretches and other things to keep his legs strong and limber. Maybe you could call the coach (on the sly, if your son won't do it himself) and see if he will approach your son with some suggestions. Knowing his coach has hopes for your son's eventual return to running (spring track, maybe?) might be enough to kick your son into gear. Maybe he can participate in other ways - help with stopwatches, encourage other runners, learn the specifics behind different muscle groups and oxygen use, whatever the coach is teaching the rest of the team.
Obviously, if this goes on for a long time or you see signs of great concern, you should look at having him talk to a counselor. But maybe he'll kind of get bored with his self-pity and snap out of it, at which point you can give him credit for doing an adult-like thing and seeing the big picture.