I don't think there's anything more... final than the loss of a pet. As has been said, when you love something so purely, and it loves you back, simply because you exist, well... there's no feeling quite like it in the world.

And the worst part is truly as you have said - that terrible feeling when you remember time and time again, when you wonder where they are, or what they could be doing. The pain of knowing... it's crushing, and it hurts, and it's a loss - dog, human, cat - all are losses that need to be grieved for, and no one faults you for that. My love to you and yours.