Hi Olympiadis,
I am so sorry for your loss
I won't tell you to stop beating yourself up because, as cat (or any animal) lovers, it's what we do.
But as i went through the losing my little Phoebe 3 months ago, i know that these type of thoughts are inevitable. It seems to me you have done the very best for your Mac, given the situation and you had no control over his illness. You had already had to take him to the vet twice in one week, and it wouldn't have been fair to keep doing that, so you did the right thing for your little man. Animals are wiser than we think and he would know that. He was very lucky to have you and i believe our pets never leave us, they are waiting for us! Google 'rainbow bridge', i found that really helps when i am really down.
It will get easier, and please go easy on yourself.
Fellow animal lover.