How do I explain this?

We get a lot of birds in the yard. One time we even had one crash into the slider. Scared the crap out of me. A couple of weeks ago, I decided to get a bird feeder so the kids can watch the birds eat. Eventually I'd like to get a bird bath, but for now watching the birds flit around the yard is good enough. Even Taede enjoys watching them.

The feeder:

Bird watching is so enjoyable and relaxing. I've noticed more birds singing during the day so there's that element too. Kael dug up his binoculars and he's getting a kick out of watching the birds really up close. We even get a couple of doves pecking at the seeds on the ground.

Like I said, very relaxing and enjoyable.

Until this afternoon:

Can you see what I'm seeing? I noticed a mass of gray stuff on the ground this afternoon and upon closer inspection, I realized the gray stuff was actually a bunch of FEATHERS!!

Holy crap!! Something caught a bird and ate it!! I frantically looked around, hoping to not see a carcass, thanking my lucky stars the kids were still in the house. I didn't see anything, but I didn't look quite as carefully as I would have liked either. I had to beat feet it back into the house before the kids wanted out.

So now I don't know what to do. Do we keep the feeder, feeding the birds but at the same time making them, well... sitting ducks for a predator?

Ugh. I feel so guilty.