Former Manchester United star Cristiano Ronaldo grabbed the winner in stoppage time after having an effort beaten away by the inspired Hart - one of several fine saves by the keeper - moments earlier.
Hart told ITV: "You can't go 2-1 up with five minutes to go and lose the game. Who else can we blame? We can only blame ourselves.
"We dug deep, got a lead twice and we lost it, so we can only blame ourselves.
"It's hard to come off the field after losing 3-2 and be positive. I'm really sorry.
"We're not a team that should come here and pat ourselves on the back for doing well. We're a team that gets results."