Some minor crying is pretty normal the first night. In addition to the pain, he has to shake off the anesthetics which can cause upset stomach. If the vet sent him home with pain meds, give them as directed.
My vets have always said not to worry if the dog doesn't eat until the following day as long as the dog drinks some water. If he doesn't want to eat tomorrow, a call to the vet for advice is a good idea.
Cones are annoying but important until the area is healed. If the cone is the kind that the dog cannot see through, I'd suggest grabbing a see through cone from petsmart/etc so the dog is less disoriented.
Most likely though for a normal male neuter, he will feel much better in the morning and the hard part will be keeping him calm for a week of no jumping or playing.
The whining, crying, and not wanting to eat are more than likely after affects from the anesthesia. I've had lots of animals spayed and neutered, and have never had to use an Elizabethan collar. Personally, unless he is just really going after the surgical area, I'd just take it off, as it can cause more distress than it's worth.