I've just started playing sims 4 for the first time and I actually got really sad when my pet ran away cause I told them off for playing in a puddle.
Oh wow! What did you do when your pet ran away?
I was really sad when they ran away, because I yelled at them for getting my floor wet.
It's normal to get emotionally attached to the characters that are in role playing games. As long as you don't become obsessed with the characters from the game, it's perfectly fine to feel emotions such as sadness with something negative happens in game.
Nah man...I'm so bummed out about it.
It's okay to be a little bummed by it, but it's just a game and you can always just start over and get a new pet.