Guilt

I am very very sad about Bit.  Paralyzed, to be honest.  I have a difficult time sleeping, a difficult time waking, and a difficult time doing anything.  While I'm sad that he's gone, and I know that he was in a very bad state, I still feel guilt.  I feel that I let him down, that I gave up on him.
The fact of the matter is that Bit was dying from Cancer.  It was going to get him at some point in the near future.  I had expected sometime around the end of the year, so this definitely caught me by off guard.  He was sick, getting sicker, and going up and down with alarming frequency.  He was tired, and in the end, he was suffering.  I ended his suffering quickly and painlessly.
But the "quickly" part is what's bothering me.  Did he have another month or 2 left? Might he have recovered?  The answer is "maybe", which is the part that's killing me.  Of course, what a 'recovery' may have looked like is not ideal - a regimen of subcutaneous fluids, supplements and appetite stimulants, medicined for his bowels, steroids.  In other words, a very medical existence.  While he would have had a few more weeks to put his head in my hands, it would have been for me, to hold him.  To sit with him. To worry that one night, I'd come home to him dead or dying or in some great distress and then to do the rush to the vet in the middle of the night or some other time and to have a nameless vet put him down.
I opted to end things on Saturday. I've been told I did the right thing by everyone.  But I'm having a hard time internalizing that, believing that.  I wake up saying "I'm sorry, I'm sorry."  But I knew.  And he knew, and L knew and the doctors knew.  But that's the head.  The heart, the heart wants to believe.