I'm quite behind, so someone probably has already said this...but:
You are human - humans feel emotions and express them!
Crying is a way of expressing deep sadness and loss - it is both okAY, and also part of the healing process. Ever species mourns in it's own way - I have most definitely seen my chickens mourn. Don't be afraid to be human and mourn in a human way - crying. It doesn't make you less of a person, rather more of one who is willing to recognize their feelings.
I am sending warm, heartfelt hugs to you!