Heads up nut flush with ugly river

ok sorry the ace on the flop was a heart giving me the nut flush..not that it matters at all mostly worried about the boat though. I was pretty sure I was beat there but couldn't get myself to fold, he showed A4 for the boat and took it down. Looking back this hand troubled me a lot, I just dont see anything that I have beat playing it this way, but in heads up I feel too weak tight folding here.