I had to do it !!!

Maybe I'm wrong, but the difference between your picture and mine is the distance the animals (and the camera) are from the fence. In my picture the cat face is right on the fence, the DOF covers it.  In your case the peacok was probably away from the fence, 2 -3 feet and you can blur the fence easily by going manual. I also captured the fence intentionally, I wanted to show how the animal is inside the enclosure, trapped in there.

Carlos
http://www.charlysworld.com