To add insult to injury, Oli McBurnie was dismissed for dissent in the 14th-added minute.
The Blades did their best to run down the clock during the 90 minutes, which they "won" through a Gustavo hamer goal, but it came back to bite them, with Richarlison and Dejan Kulusevski scoring late goals.
Heckingbottom was furious at the way Peter Brookes officiated, claiming the referees are dictating how his team plays and do nt understand the game.
"It's not funny, the refereees are killing the game at the minute – absolutely ruining it," he said.
"I've no qualms about the result.
"From 0-0 I was telling our keeper to hurry up. We split (centre-backs) to play out (from goal-kicks). We play to Anel (Ahmedhodzic), we play to Bash (Chris Basham), and we play forward.
"We get out a couple of times so Spurs change. We put the ball down, Spurs change, so Wes has to make a different decision and he’s getting told to play. Why would you play then? Spurs have adapted to us so we have to change again and play something different.
"When he handles outside the box he gets booked. I've no problem with Peter but the referees are just showing how little they know about the game and they're directing it. How can that possible?
"I wanted to show them at half-time but I know they can't see it.From the moment it's down we're taking it in 10 seconds but because we're getting out and playing to Oli, Spurs change so Wes has a different decision to make.
"He can't make his decision until Spurs have moved. The referees haven't got a clue, they don't know what I'm saying.
"The answer back to me was, 'Kick long, then.' We work all week on how we want to play and the refs are dictating to us how we play the game. It can't happen but it's happen."
His unhappiness with inconsistencies was not limited to McBurnie's second yellow card, and he claimed it is making it impossible to coach players.
"Cameron (Archer) catches the ball first half because he's deemed offside," he said. "He says to the ref, 'I'm not offside' and he gets a yellow card. It's not time-wasting.
"Understand what you're actually doing.
"At the minute it's really foolish.
"We've taken VAR away so it's back to the referees, fine. But then the referees need to be really consistent with their decision.
"I couldn't tell you want a penalty is, it's different game on game.
"I'm coaching players and I couldn't tell you what a penalty is, whether it's handball or a trip in the box. How can that be right?
"They (the Professional Game Managament Officials Limited) listen but they've got to understand and for me to be told at half-time play long then, what is going off?
"It's foolish. The ball boys are literally laughing at the referee, they're taking the mickey out of them."
It is hard to see how Heckingbottom's comments will not earn him a heft Football Association fine but he did raise some important points.
As for the game itself, Heckingbottom was largely pleased by a spirited display, but admitted it was undermined by conceding two cheap late goals.
"As I said before the season started, the league, the teams, won't scare us but we know we have to be really good to compete," said Heckingbottom.
"We were close to all three points then it looked like one and it's non and that's how cruel the game can be but you've got to expect that can happen against these teams. Ange has just won manager of the month, Maddison was player of the month and they're in a real good place.
"You could see by how they celebrated how close we'd taken to the wire and how hard we made them work.
"We accepted we had to give up certain things but for the majority of the time that worked and their efforts were from outside the box.
"I know Wes played exceptionally well until the goals but especially second half their efforts were from outside the box, which is what we would have taken.
"Spurs aren't going to let us win the game, they're not going to let us take a point, they're going to fight until the death.
"It's a couple of lapses in concentration, that's what it was, but Ange will say his team's gone to the death and they have, they've done great. They never stopped and they ended up taking the points."