You're darn right you can't...that's hypocritical. To say "oh I like this animal and that animal and nature, but can you kill off THESE animals please? I don't like them very much....".
I'm curious: In what way are they costing you thousands? I have a big ol raccoon who comes to my patio door once in a while to check in on my cat. He walks up the stairs, across the deck, and down the other side. No damage no cost. I have deer that use my backyard as their own shortcut to the provincial park along the way. I tell you, last winter there was a path about 4' wide where the snow was trampled down almost to the grass.
Things you can do to discourage them:
1) Pick up some water cannons. They are motion controlled and spray the area whenever something walks by the motion sensor. Friends have them up here to discourage deer from eating all their flowers and if you forget, it's like navigating through claymores approaching charlie's village....
2) Make sure your garbage is sealed air tight and INSIDE. They come around looking for food and or shelter so if you don't provide them with either, they won't bother you.
3) Make sure you keep your grease cup and your BBQ spotless. Grease and food remnants on the grill will draw them like flies.
You might want to try one of these too:
http://www.amazon.com/dp/B004VNDXLU...tiveASIN=B004VNDXLU&adid=06NCWDJRXGYFEEGD257H
or one of these water cannons:
http://www.contech-inc.com/products/scarecrow/
I tell you, they work. My friends have a nice pretty garden free from deer shit.......