If you wouldn't feel sad, you wouldn't care.
Consider this: You can't safe them all, but if you safe one, you safed a life and one less will die! If you tell your friends/family (called Crossposting), maybe the flow of information will safe another!
If you spend the time to give an animal comfort during its last day(s) on Earth, you may have eased its pain/fear.
If you care enough and have the means to do so and you help spread the word about them (crosspost), help organize transport, rescue, foster homes or just simply give them some comfort and care, you've done a great thing!
Rescue is not about being a Lone Ranger! It is about being a part of a Team and as such work together to make things better.
The first step is to care and to feel sad! It means that you see them as a life, not an object!