I'm so sorry. My deepest sympathies go out to you and your family. My husband once said (after his mom passed away) that the reason why we cry after the loss of a loved one (human or pet) is because it will usually take us many many years before we meet with them again. However, to them, it's only a matter of seconds, so they don't feel the pain that we do. Please know (and I know you do deep down) that you made the right decision for Murphy (the ultimate act of love for him) and I'm sure he's feeling much better now and will be waiting for you with a kidney bean and sloppy kisses!
All my love and prayers to you Sarah,
Jo-Ann