Although Heckingbottom has told The Star he plans to lead from the front following his appointment last month, the 44-year-old also wants those under his command to take responsibility for how the rest of the season unfolds.
After making a slow start to the campaign - something both Heckingbottom and his predecessor Skavisa Jokanovic attributed to the manner of their relegation from the Premier League last term - United have now won three games in a row - including two since sacking the Serb amid reports of a difference of opinion about transfer strategy with members of the board.
“I’ve let the players know this is their team,” Heckingbottom said. “They have to own their standards and everything they do.
“We, as a management team, set them. And then what we do is reward the people who adhere to them.”
United return to action following last weekend’s victory over Cardiff City when Queens Park Rangers visit Bramall Lane on Monday. That fixture marks the start of a critical period of matches, with leaders Fulham next on the agenda.
QPR are fifth, six points ahead of United who climbed to 10th after putting Steve Morison’s side to the sword.
“Standards have got to be kept high,” Heckingbottom said. “I’m delighted with how the lads have responded. But we’ve got to keep on striving and trying to get better.”