Backed by 4,300 fans, Stags were sunk by a Craig Mackail-Smith goal in a game in which they failed to register a single shot on target.
“I won't accept a performance like that again, whoever we play,” said Flitcroft.
“In am bitterly disappointed for the town, our supporters and our owners. We didn't represent them today.
“Our supporters came across in numbers and paid good money today and represented the town with the passion and commitment they've shown all season. But we haven't replicated that.
“They know how I feel about this. I feel let down and they have let each other down.”
Stags' players have shown their quality in reaching second place in the table. But today Flitcroft said they lacked the other side of the game needed to win a derby as Notts simply showed more commitment.
“When you have quality players like we have, the test every time every time you train or play is to make sure you commit to the other elements of the game out of possession,” he said.
“You have to make sure you are mentally right, mentally focused and mentally competing.
“It's easy for me to look at that as a player who didn't have much quality. But one thing I always gave was 100 per cent – I understood that.
“Today we didn't commit how I wanted them to commit and we were not brave.
“We didn't have the mental toughness to get on the ball and really cause them problems. All over the pitch we were half a yard off it.”
He added: “Yes we are up there near the top of the summit, but we won't rest on our laurels.
“I have to make sure this group understand that and what makes the greatest sportsmen the best – work and commitment – the two ingredients of every success story out there.
“You have to earn your inches on a football pitch and then you've got to earn your yards, and we didn't.
“We have had one shot and that wasn't on target. Apart from that we have not got in and around them.
“You have to do that in any football match, let alone a local derby that means so much to so many.
“Notts looked like they wanted to compete and they were almost free while we played with a bit of fear.
“When you are playing with fear and anxiety, physically your body sometimes doesn't work and that's what it looked like today.
“We were not brave enough. We let people die on the ball. It was a massive game and we didn't turn up.
“We never used the width where the space was and we were nowhere near Mackail-Smith for the goal. He is 19 yards out and someone has to be in that vicinity.”
The Mansfield players now face a tough seven days before next weekend's home clash with Forest Green.
Flitcroft said: “I have spoken to them about what next week is going to look like. I want a massive response from this huge disappointment.
“It's got to be a 40-50 per cent improvement on today's performance.
“It's going to be a long week and maybe a different commitment than I have asked of this group this season.”