United fell behind after 16 minutes when Jon Bodvarsson finished an incisive Royals breakaway but Pontus Jansson tucked away Adam Forshaw's cross to level matters two minutes before the break.
A fine strike from Pablo Hernandez then put the Whites 2-1 up four minutes before the hour but United then allowed Reading to equalise just two minutes later when a Leeds free-kick led to a Royals counter which ended with Eunan O'Kane scoring an own goal.
"I'm aggrieved because their second goal is upsetting me," said Heckingbottom.
"Just because initially it is from our free-kick.
"We decide to play a quick free-kick which is fine.
"We've got three men behind the ball and they have got none in front but as we play the ball forward our three run forward and Mo Barrow runs forwards so when the keeper eventually claims it we give him the option to go and hit us quickly on the counter.
"It's those little details that have been costing the team throughout the season and those things that we have to iron out because the players were oblivious to that and I pulled them on it after the game.
"You can be so ruthless by getting those things right because we had worked our socks off to get back in the game and I felt we were the stronger team in the second half so that's why I am disappointed."