He should feel horrible, and mostly he does.
He's lost her, and she was Rose, and he's not really sure what he's going to do now.
But somewhere inside him a guilty thought points out that it's probably better this way; because now, now she'll always be twenty and brilliant and in love and alive.
And he can't stop the selfish little part of him that says that this couldn't possibly hurt as much as watching her grow old and bitter and leave him. It can't hurt as much as watching her die.
He shouldn't be relieved, but he is.