Most likely he ate something that isn't agreeing with his system. Puppies eat anything they can get their teeth on. If his nose is warm, and he's still got the diarrhea, I would then take him to the vet.
It could be something more serious, but generally, when an animal gets their shots, they are checked out to make sure they are healthy enough to get them.
Sometimes, they do miss something though, that's why I recommend getting puppy to the vet. Hope this helps, good luck.