The Blades showed great character, good defensive organisation and in the second half, positivity, as they took on Chelsea in Sunday's Stamford Bridge quarter-final, but Heckingbottom was busy talking to the media when he thought he should still be shouting at his players from the technical area, having done enough to earn extra-time.
David McGoldrick missed a great chance to cancel out Oliver Norwood's first-half own goal with a diving header, and Hakim Ziyech's added-time goal gave the scoreline an extra gloss which was perhaps unrealistic, as the Blues progressed to Wembley with a 2-0 win.
“It was a tough one to take,” interim manager Heckingbottom admitted. “It's bitter-sweet because we've been knocked out of the FA Cup and I thought it was there for us. It wasn't for a lack of effort or quality.
“We know why we're not still playing, we know why we've not gone through.
“The game was there for us, what an opportunity.
“I think I'll get more and more disappointed as the day goes on. We could have, should have won the game.”
Chelsea utterly dominated the first half in terms of possession, but the Blades excellent defending limited them to one shot on target, from Christian Pulisic, and Norwood's 24th-minute own goal.
But the visitors showed a much more positive mindset in the second half and it was hard to argue with Heckingbottom's assertion that they were the better side in it.
As well as McGoldrick's header, Oli McBurnie had a shot saved, Enda Stevens headed a Norwood free-kick narrowly wide, and substitute Rhian Brewster put a deflected shot into the side netting.
“I thought first half there was nothing it it, we defended well and didn't let them play through is but I thought we were poor in possession, weren't brave enough in possession and didn't press high up enough in the pitch,” said Heckingbottom. “We demanded more bravery.
“The most significant difference was we were better with the ball, which allowed us to be the better team in the second half.
“We were getting into positions, making half-chance, we were building momentum and the big chance fell to Didz (McGoldrick) and if I was putting my money on anyone (to score), it would have been him.
“In terms of the performance, I was really pleased with the boys.
“I want them to play with freedom and be positive. What have we got to lose?
“We have to pay with a freedom, a spirit and just take the shackles off. I've told the players I'm not going to criticise anyone for giving the ball away, the problems are when people don't want the ball in the first place.
“In the first half, the biggest problem was we weren't good enough with the ball. I knew we were capable of doing it and the players have shown it.”
The Blades were without two of their most experienced players, with muscle injuries seeing Billy Sharp and Chris Basham added to the already lengthy list of absentees.
“Sharpy's going to be out for a few weeks, Bash we had to pull out last night,” revealed Heckingbottom.
“We wanted to keep the same shape. We could have changed to a four but we'd not worked on it this week.
“Billy's (injury is at) the top of his thigh, Chris got a kick in training at the beginning of the week which hasn't settled down. We don't know if it's bleeding (internally) but it's a blow because he's been a huge part of it.”
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