Yes animals can and do cry when they are sad.
You may not notice an animal crying when they are sad like you would notice a human cry when they are sad.
However I can notice when my dog or cat is sad and crying.
When my dog or cat is sad and crying I will notice a sad looking face and notice some tears in the dogs and cats eyes.
The animals don't cry just like humans do but animals can and do shed tears when they are sad and need to or want to cry.
It's okay for anyone to cry including humans, adults, kids, teens and all animals.