Having got back on level terms through Jayden Bogle's equaliser in a game where the treble winners utterly dominated possession, City won it when Kyle Walker beat Yasser Larouci to the ball at the touchline and his pull-back bounced off Phil Foden for Rodri to lash home.
"I'm pleased with the performance," said manager Heckingbottom. "(But) you need a perfect performance to beat them.
"We get punished for two things we should do better but the sickener for me is how Rodri's lashed it in. It comes after Phil miscontrols the ball and it drops straight into his path which is a kick in the teeth after all the good play we dealt with.
"We've lost a point but we'll focus on the performance.
"Game on game we have got better on better and I certainly believe we're going to have more than enough, I certainly believe we're going to cause teams problems and we're improving.
"The crowd were first class from the beginning to the end. I've said all along we're not going to change our approach, we're going to give everything in every game
"What will keep me awake at night is not getting to the point where we were making the changes at 0-0."
They did not because Erling Haaland made amends for hitting the post from a first-half penalty by nodding in a Jack Grealish cross. At that point most people would have assumed the floodgates would open but the fit-again Oli McBurnie and Bogle came off the bench to have a big impact, the latter a goalscoring one.
With Cameron Archer's £18.5m move from Aston Villa completed in the morning – too late to feature in the game – Heckingbottom's attacking options should be much better for next Saturday's game at home to Everton.
"It's been tough for Will (Osula) and Benie (Traore) in every game – they've been asked to do the legwork, the hold-up play and be the goal threat," said Heckingbottom. "Will's made three league starts at Derby (on loan last season) before here, Benie's played not much more in Sweden at Hacken.
"We are in a position to give them more help now so you'll see a lot more of them with a bitm ore experience around them or us with a bit more control of the ball in games or them impacting from the bench."
Having conceded 80 per cent of possession and 30 shots, the Blades could hardly complain the result was unfair but were aggrieved at the first-half penalty which saw Julian Alvarez's cross strike John Egan's hand away from his body as the defender tried to steady himself off the ground.
The maddening inconsistency of the video assistant referee system is annoying Heckingbottom.
"Is there any point having VAR if the same decisions aren't given every week?" he asked.
"I guess we want as little impact as possible from VAR but (if so) just get rid of it.
"We need a degree of consistency, especially on decisions that change games.
"A few years ago we had it, now we've not had it for a few years and we've got it again.
"It's changed every season – how it's going to be used, how it's going to be interpreted. It's changed again.
"If you speak to any of the guys we just want the same decisions to be given.
"We're coaches, we want as much control as possible on our team so we need to know what the laws of the game are.
"We've had three games now and even in our games we've had decisions that are not consistent.
"I wasn't happy with the refereeing today, I'll be honest.
"For us to get our first free-kick in 56th minute is embarrassing. I have watched some decisions back, it's really poor."