My dad died from cancer in November.

he had a lump on his back in summer and after finally being seen by the right department it was removed. 
dad was then sent for a scan of his chest as they suspected it was skin cancer. 
we got a call the following week to say there was cancer all down into his lung. We were being referred urgently to the resp doctor and would get an appointment within 2 weeks. 
I got my dad put on morphine and we were with him each day, but we never got to the doctors he died 1 week after that call. I had been there all day, took my children after school to see him, when I went the next morning he had passed away. 
there was some blood around his mouth, on the pillow/bed. 
my brother didn't want a post mortem, I sort of did but went along with it as the thought If dad being cut really upset me.  but I wonder every day what happened. He was up in his chair laughing with us the night before. 
he was in pain and had lost weight, a little confused but he just didn't look like he was going to leave us yet, his referral to hospice at home was rejected as it 'wasn't time yet'. 
when I rang the lady who was to be coordinating his care she said she had wondered when I spoke to her if he had a slow bleed!?!? would he have passed more peacefully if we knew this. I miss my dad and I beat myself up every day , he might have been shouting out for me and I wasn't there. 
there's so much more, and so many missed opportunities by drs/nurses/respiratory/ mental health teams to get dad an earlier diagnosis and treatment.

I wonder if anybody has similar feelings and how they manage it. I spent so so much time with my dad and feel heartbroken I wasn't there when he left us.