Heckingbottom's current team were labouring in the first half against his old club and even at the start of the second, but took control once Sander Berge put them in front after 55 minutes.
"12.30 kick-offs can be like this, stadiums can be quiet, it can be flat," said the Barnsley-born manager. "I understand why we do it for police reasons but it does affect atmosphere.
"We looked like the team that played Wednesday night (at Blackpool), then had the turnaround to a 12.30 kick-off.
"Half-time was not much tactical, it was about the mentality, not wasting all the hard work we've done in the last few months and seizing the opportunity.
"We demanded a quicker pace with and without the ball, risk-taking, moving the ball quicker.
"We did that from the first whistle (of the) second half. I thought Barnsley stayed with us for the first 10 minutes or so but then after the goal we took control of the game."
Berge's goal was his third in four games and they added to it with one for Morgan Gibbs-White.
It pushed the Blades up to fourth in the table ahead of the 3pm kick-offs.
The only concern for them was a second-half hamstring injury to Billy Sharp, who was quickly replaced by Daniel Jebbison.
"He's felt something," confirmed Heckingbottom.
"Me sitting here now, if I'm totally honest I'm anxious about it. Probably the positives if I really think sensibly about it, Billy's experienced enough to know his body and as soon as he felt something he signalled over and stopped. He knows not to carry on with anything muscular.
"He'll have a few days' rest and recovery and we've got a scan booked for later on in the week and we'll take it from there."
The Championship now takes a two-week hiatus for international football to take precedence.