But manager Billy Dearden and the home fans will be proud of their side's endeavours against their multi-millionaire opposition, 78 places above them in the league standings, as they pushed them all the way.
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Indeed only the crossbar prevented Stags hot shot Michael Boulding levelling it and, with any measure of luck on another day he might have had a hat-trick as he also forced Mark Schwarzer into a good save and put another effort narrowly wide.
As a spectacle for the watching Match of the Day live audience, and the biggest home crowd of the season - 6,258 - there were few clear cut chances at either end.
But Boro took one of two good chances to come their way in the first half as Korean star Dong Gook Lee grabbed a 17th minute opportunity and later wasted another from a free header.
With Stags doing most of the pressing after the break and the visitors under pressure, the crowd remained on tenterhooks until the killer blow came three minutes from time when home skipper Jake Buxton could only help George Boateng's lob into his own net.
The home players gave excellent accounts of themselves with midfielders Stephen Dawson and Matt Hamshaw really catching the eye.
But with German star Robert Huth and promising youngster David Wheater in commanding form in the heart of the Boro defence, the visitors managed to shut up shop and avoid any embarrassment for boss Gareth Southgate.
It was the second time in three seasons that Stags have narrowly gone out to North-east Premiership opposition after their exit at Newcastle two seasons back.
But with the Cup hype now out the way it is time for Dearden to quickly get his young charges focussed on Tuesday's crucial relegation battle at Lincoln.
Hopefully this display will have lifted each and every one of them for that clash.
Stags named an unchanged 16 from last weekend.
Boro fielded a very strong line up with Tuncay the only notable absentee and Boateng and Downing starting the afternoon on the bench.
Stags started brightly and Huth had to produce a diving header to clear a dangerous first minute cross from Dawson.
The ball wasn't cleared far and Boulding eventually cued up Hamshaw but his shot was sliced and harmlessly wide.
Dawson was lectured for catching Rochemback late with a tackle and Jelleyman cleared the long free kick as it bounced in the home box.
Johnson showed neat footwork to dance between two home players and tried to send Aliadiere on his way in acres of space on the right. But Jelleyman stretched out a leg and produced a crucial interception.
Cattemole won the visitors the first of two successive corners on 16 minutes. And the visitors grabbed the lead from the second on 17 minutes.
Johnson floated it over, Muggleton tried to punch clear but failed, creating a scramble in which Wheater had an attempt blocked but the ball ran to Lee who made no mistake from six yards.
Boulding almost got away onto a long searching Bell ball, Schwarzer having to leave his box to clear.
Stags' first corner saw Hamshaw pull it back very deep for the incoming Dawson. His accurate cross was headed out to Bell who crashed a hurried shot over the top.
Boro replied with a good run by Aliadiare as he cut inside on the right along the by-line and pull back towards Arca who hooked his first time finish wide of the near post to Mansfield's relief.
Boulding looked to have good claims for a penalty when two defenders seemed to lean on him as he strove to reach Buxton's cross, but the game went on.
Bell gave away the ball to Arca on the edge of the box and Buxton did well to get his chest in the way.
Huth saw the first yellow card of the game on 27 minutes for a nasty lunge on Boulding with the home fans chanting for a red card.
Rochemback put Boro's third corner into the near post where Huth headed wide on 30 minutes.
But Stags came so close to levelling the game on 35 minutes. Boulding accelerated down the centre and let fly with a dipping shot that clipped the crossbar.
The referee decided Schwarzer had got a touch and awarded a corner which saw Boulding get in an on-target header that forced Schwarzer had to stretch up to keep out. Finally Brown scooped the ball over on the turn.
Boro should have strengthened their grip three minutes later when Aliadiare again got to the right by-line and sent in the perfect cross for Lee who sent a free header wide from six yards.
Bell was wide with a hopeful effort from 25 yards after neat work from Hamshaw on the right for the home side.
Hilariously the game was held up at this point by a succession of footballs being kicked into the ground over the top of the Bishop Street stand with various anti-Keith Haslam slogans on them.
The serious action resumed with Stags clearing another Middlesbrough corner.
Schwarzer was lucky not to be punished when he sliced a kick badly and the ball span up in the box with no home players near.
Bell then robbed Cattermole on the edge of the box in stoppage time and fed Brown who was quickly crowded out and finally sent a tame shot towards the keeper.
Boro changed things round at the break with Boateng on for Pogatetz and Arca moving to left back.
Martin did well to block Lee's strike from Boro's first second half corner.
Brown should have done better with a through ball with Boulding and Hamshaw making runs but it lacked any pace and was easily cut out.
Hamshaw won Mansfield a corner which the visitors laboured to clear and Dawson finally blazed over from 25 yards.
Then Hamshaw got to the right by-line and crossed hard and low to the near post where Boulding's flicked finish was wide with Huth in close attendance and Brown in a good position beyond him.
But this was stirring stuff from the League Two strugglers who looked determined to find a way back into the contest.
Dawson slipped Brown into space on the right inside the box but he seemed to be looking for the penalty as Arca slipped in and the referee decided the Boro skipper had not deliberately upended him.
Cattermole went straight through Dawson as he tried to go past him down the right which earned him a yellow card.
More footballs appeared on the pitch on 63 minutes with the home fans chanting 'Haslam out'.
Boro cleared another home corner and soon after Hamshaw crossed from the right and Boulding stretched to meet it but couldn't keep it down and the ball flew well over.
On 65 minutes England winger Downing joined the action for the outstanding Johnson. Goal hero Lee then made way for Mido on 71 minutes.
Boro had not really had a sniff in the second half but could have killed the game on 73 minutes when a poor Hamshaw free kick was cleared and Arca broke down the left. Stags were outnumbered at the back but Arca's crossfield ball was poor and evaded both team mates.
Dearden made a double swap at this stage, bringing off Bell and Brown and sending on McAliskey and Arnold.
Martin was booked for a spectacular rugby tackle as Rochemback tried to turn him and go clear from the centre circle.
Arnold went on a promising run but the ball caught in his feet and he ended up squaring to Boulding who rifled a shot wide of the near post.
Stags won another free kick on the right but Martin, like Hamshaw before him, failed to even clear the first defender's head and Boro cleared.
Indeed, they broke quickly and the move ended with the killer second goal.
The visitors spread the ball from left to right and Boateng floated it back over the stranded Muggleton where Buxton tried to intercept but could only succeed in heading into his own net.
It was a disappointing end to a courageous performance from the plucky Stags.
And while another round would have been very nice, this FA Cup exit was far from the end of the world with such a battle ahead for League survival.
STAGS: Muggleton, Mullins, Jelleyman, D'Laryea, Bell, Hamshaw, Dawson, Brown, M. Boulding, Buxton, Martin. Subs not used: White, McAliskey, Arnold, Holmes, Wood.
BORO: Schwarzer, Young, Arca, Pogatetz, Rochemback, Aliadiere, Huth, Lee, Cattermole, Johnson, Wheater. Subs: Turnbull, Riggott, Boateng, Mido, Downing.
REFEREE: Steve Tanner of Somerset.
ATTENDANCE: 6,258 (1,364 away).
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