Everybody absorbs it differently.
There are also many factors that determine how our minds and bodies respond to it. Whether the person or pet had lived a full life or was young, how they died, where they died, etc.
When my grandfather died of Alzheimer's, the family was somewhat at peace because he was no longer suffering and we had been given years to mentally prepare ourselves. Very few of us cried. We were proud of him and the life he lived and were glad he was finally at peace. When my 16 year old dachshund died of kidney failure I cried like a baby for the whole evening but moved on the very next morning. A few months later, a relative died unexpectedly and in my arms at 2 o'clock in the morning. I didn't sleep for 40 hours, forgot entire days, and over the next two weeks I woke up covered in sweat and screaming into my own hands.
It's part of life, and it's one of those things that can easily get either worse or more tolerable as you encounter it.