Stags lost on penalties after a thrilling 120 minutes ended goalless and Flitcroft said: “Our dressing room is back to back with Newport's so I told the players keep quiet, listen, absorb it, understand it and come out of that fighting.
“Don't ever have this experience again. It's horrible and cruel. I felt sick listening to their celebration.
“It just comes down to big moments and 95 per cent of our season I'd find it difficult for anyone to argue that it's not been good.
“Our standards have been consistent and good. It's the other five per cent that we've not done that's not got us over the line. That's the bit we need to improve on for next season.”
READ THE REPORT HERETwo major decisions went against Mansfield in the first leg with County lucky not be down to 10 men early in the game and then gifted a penalty that replays show wasn't one.
“I felt a bit hard done by over the first leg at Newport,” he said.
“I have had an apology from the Referee's Association about the two incidents they got wrong. So this could have looked different. I really wanted to bring home a lead into the second leg.
“But tonight you've seen two sets of players and staff go all out full throttle to try to win a game of football and how a goal wasn't scored in open play I haven't a clue.
“It was like a slug out. We left ourselves open and vulnerable at times and so did they. We have had good chances.
“The lads gave it everything they had – they left it all out there. That's all I can ask of them.
“Massive respect for Newport. They gave us one hell of a game here as they did there and I wish them well at Wembley.”
Stags were without influential midfielder Neal Bishop after he was ruled out with injury and Flitcroft admitted: “He was always going to be a miss.
“It was a late call. He had a fitness test. He tore his calf in the first leg and just couldn't get it going.
“He tried everything – tablets and injections – but he was still struggling. He has been a driving influence all season.”