You are the best judge of how much information your children can handle about death and the loss of their pet. Don't underestimate them, however. You may find that, by being honest with them about your pet's loss, you may be able to address some fears and misperceptions they have about death.

Honesty is important. If you say the pet was "put to sleep," make sure your children understand the difference between death and ordinary sleep. Never say the pet "went away," or your child may wonder what he or she did to make it leave, and wait in anguish for its return. That also makes it harder for a child to accept a new pet. Make it clear that the pet will not come back, but that it is happy and free of pain.
Never assume a child is too young or too old to grieve. Never criticize a child for tears, or tell them to "be strong" or not to feel sad. Be honest about your own sorrow; don't try to hide it, or children may feel required to hide their grief as well. Discuss the issue with the entire family, and give everyone a chance to work through their grief at their own pace.