It is a sad but common case. As you mention, people want to help...perhaps somehow distributing leaflets about your sanctuary and that you will take injured creatures may help.
Many people are not aware that they they can call Sanctuaries like yourselves for advice.
Leaving leaflets in shops etc, or even asking local schools if you can give a little talk and maybe bring along an animal or two to explain responsibility could help enormously. 😀
We do it. There also were several TV programs about family shelters in our country. We try to teach people how to help birds and animals.