The puppy is a baby pack animal, and he instinctively cries when he is separated from the pack. That's his way to let the pack know where he is, so he can be found and returned to them. However, if you are crate training your puppy, he must always be in his crate or tethered to you so you can correct his mistakes. You want to teach him to sleep in his crate and only cry if he has to go outside and eliminate. Better yet, take him out before he cries.
Buy a crate for the puppy. It needs to be small. An adult sized crate may encourage puppy to potty at one end and sleep in the other. If you have an adult-sized crate or will need one later, get a partition for it so you can keep the puppy in a small area. It will feel cozier to him and make him less likely to cry.
Play with the puppy and wear him out before bedtime to increase the likelihood that he will sleep without crying.
Give him food and water in his bowls, and then take the bowls away before bedtime. If he is fed and hydrated, that is one less reason for him to cry.
Take him outside immediately after he eats or drinks, or after he wakes. Use the same command consistently like "Go potty." Wait until you see him start to go and then say "Go potty, " so he will associate what he is doing with the command. This will come in handy later when the weather is cold, or you're on a schedule. The puppy will learn to go on command. If he does not have a toilet emergency, you'll know that's not why he is crying.
Praise him lavishly when you can tell he is finished eliminating. Don't wait until he starts playing. He needs to associate the praise with going potty.
Put the puppy in his crate to sleep or anytime he won't be with you. You can give him his favorite chew toy to keep him busy so he won't cry.
Put the crate in your room if possible at first. He will be comfortable knowing he is with his "pack" and won't be crying to be found. Later, you can start moving the crate farther and farther away from you.
Set your alarm so you can get up and take the puppy out of his crate and outside to eliminate before he starts crying. If you are proactive, he won't have to cry. When he is done, you can put him back in the crate with his special chew toy. If he does cry and it's not a toilet problem, leave him in the crate and say "No, sleep."
Keep the crate in another room if necessary. Put a ticking clock in the crate with him, and a small piece of clothing you have worn. Not a blanket, because if he has an accident on the blanket, he can cover it up. You can also use a radio to soothe him.
Don't give in. If you know the puppy has had food and water, and has been out to go potty, then don't go to him when he whines. He wants attention, and if he gets it, you are reinforcing the crying.