I don't think a filter would have changed the busy background much. I went to your flickr site and looked at the exif data of a couple of these. One was shot at 300mm and one at 110mm. The exif was a trifle confusing as it thought your lens was either the canon EF 85 L or a sigma of some sort. Which I thought pretty funny considering both photos were shot at well over 85mm!
I'm guessing you're using a 70-300 lens. If it's the canon EF 70-300 f/4-5.6 IS USM, most folks say its sweet spot aperture is f/9.0.
If your lens is a sigma, you'll need to experiment to discover which aperture consistently gives you your sharpest focus.
You might also bump up your ISO. Image stabilization doesn't help with moving targets, and sometimes folks will turn off image stabilization so the lens doesn't work so hard. (if your lens has IS) When shooting sports I found turning off my IS gave me a higher hit rate for sharp shots. And, shooting at the long range of a zoom requires a pretty high shutter speed for clarity.
You can also pull the camera more securely into your forehead for greater stabilization, like pulling the rifle stock securely into your shoulder. And another shooting analogy, slowly exhale as you "squeeze," don't "jerk" the trigger. Er, shutter release...
Everyone who shoots birds will tell you that your "hit" rate will be dismal at first, but with practice you can get good. It's really difficult to get that focus point spot on with a small moving target.
Just hang in there and keep shooting is the advice I've heard from birders.