Wow, not sure what to tell you to do. Sounds like a bad situation. Was this a friend's pet? Did they know the risk? Did you know the greyhound would most likely chase/attack a cat?
Was the cat in the room as a safety precaution to keep the cat safe? If so, sounds like it was an accident...and the most you can do is apologize. You may want to offer to pay the vet bills.
We went to a friend's house whom has two boxers that our greyhounds love to play with. Our friends have a cat and put it in one of the bedrooms to keep it away from the dogs, we all knew that my greys do not play well with cats - hence why she was in the room. My friend went to go check on the cat and when she left the room the box in front of the door must have moved and the cat got out. Naturally my dogs went after it and bit it really hard. She was bleeding and has a big puncture in her stomach. They immediately called the vet to take her in and I offered to pay, but they didnt make it to the vet before the cat passed. I felt so bad. We all were in shock and they both kept saying its not your fault, but I feel horrible!
I agree with what you said and I feel in my heart that is what I wanted to do for them. I was going to offer to go with her to get a new cat. It is hard for me in this situation, because I am a dog lover and never had a cat. I dont know the emotional attachments that come with owning a cat.
Thank you all for your support and opinions. This helps me feel alittle more secure about my thoughts towards the situation. I, of course, want to feel as if it was my fault for this to have happen, but so many factors make it purely a bad accident.