So glad I don't have to worry about such cases. Tough situation I'm sure, especially since it sounds like you are friendly neighbors for the most part. I'd just explain that you do everything in your capability to assure a good clean kill, but every now and then one will get away from you. I'd leave it with an apology(as it seems you wish to remain on good terms), an assurance that you will continue to do everything possible to keep it from happening again and point out in x amount of years this is the first time the issue hase came about. He'll either accept it and let it go, or he never will regardless of what is said or done.