Never doubt that Max loves you and never think you've failed him!! You were there for him at the end when he needed your love the most. He crossed over feeling your loving touch. There is no greater gift you could have given him.
So be kind to yourself and be at peace on that score. Time to grieve now, but happy memories will eventually begin to ease that ache in your heart. He isn't really gone as long as you hold his memories close.
"We are--each of us--dying; it's how we live in the meantime that makes the difference."
"It's not what you gather, but what you scatter that tells what kind of life you have lived!"
"Be kinder than necessary, for everyone you meet is fighting some kind of battle."