However, the manager who has taken Middlesbrough to two of the last three finals ran it close before finally persuading his team, via extra time and a penalty shoot-out, to get him out of something approaching a personal fix.
Once the drama of it all subsided, though, he really did start to fancy his chances of going back to Wembley again. The next stop is First Division Tranmere in the quarter-finals and for some that looks almost akin to a bye into the semi-finals.
Be that as it may, neither Robson nor Arsene Wenger, his Arsenal counterpart, is quickly going to forget the climax to this night at the Riverside - or in Arsenal's case the anticlimax.
Having worked their way into prime position, Arsenal contrived to give Middlesbrough an extra bite in an unresolved 30 minutes of additional action. And when it came right down to it, Wenger's penalty-takers did not bite the bullet, but sort of swallowed it.
Davor Suker took his spot- kick in his stride, but from then on it was all downhill.
Nelson Vivas, Silvinho and Matthew Upson all stepped up to confront goalkeeper Mark Schwarzer, but two of them failed even to oblige Schwarzer to make a save.
In contrast, Middlesbrough's spot-kickers kept their nerve including Paul Gascoigne, who arrived on the scene of Arsenal's accident after 113 minutes and happily took his place in the penalty-taking queue.
To make matters worse, Arsenal now have injury concerns about their stand-in captain, Ray Parlour, who was taken off on a stretcher a minute from the end of normal time when he came off second best, in every sense, in a tackle with Boro substitute Phil Stamp. He is to have an X-ray this morning.
So hardly a night for any sort of Arsenal celebration; not even for Jermaine Pennant, who became the youngest player to represent the club at senior level at the grand old age of 16 years and 319 days.
Middlesbrough are hardly used to taking Arsenal by storm, and have conceded 11 goals in the two previous meetings of the teams.
But there were just eight minutes on the clock when the rejuvenated Hamilton Ricard made his scoring mark on the game. The Colombian accepted delivery of Deane's flick-on, turned Upson and produced a drive that had two much power in it for Manninger.
This was, in truth, Robson's second uplifting moment of the night, the first being the sight of Arsenal's newly constructed team sheet on which most of the big familiar names were missing and containing only five survivors of a team which beat Derby on Sunday.
Yet whoever they turn out, Arsenal are never anything less than worthy competitors and compete they certainly did. Not that it was perspiration that brought them their first-half equaliser, more inspiration from man of the moment, Thierry Henry.
He really did produce something out of nothing, gaining possession 25 yards out and in a flash summoning up a 25- yard drive that would have been adjudged goal of the month in just about any month you cared to name.
All in all Henry was a prime influence on affairs but not always for the reasons he would have preferred. The French striker whose season has suddenly come alive, following his two goals against Derby, was also the man behind the goal Arsenal thought had saved them from the agonies of extra time. Schwarzer was unable to hold his 30 yard free-kick allowing Suker to claim a poacher's goal after 80 minutes.
Yet three minutes later the Frenchman got himself involved in the heart of the action once too often, and with catastrophic effects. In an attempt to clear Christian Zeige's inswinging corner, Henry inexplicably handled, allowing Ricard to score his second goal of the night, this time from the penalty spot to send the tie into extra time.
What followed was a predictable frenzy with plenty of opportunities.
Perhaps the best of them fell to Suker only six yards out, but for a master finisher he made a terrible hash of his chance.
The referee, Mike Riley, seemed determined as any player to keep up with the action, and reckoned he had Juninho's measure when he booked the Brazilian for diving.
But if Arsenal's luck held out then it did not in the shoot-out.
Middlesbrough (3-5-2): Schwarzer, Vickers, Festa, Cooper; Fleming, Ince, Juninho, Zeige, O'Neill (Stamp, 64); Ricard, Deane. Substitutes not used: Mustoe, Gascoigne, Beresford (gk), Armstrong.
Arsenal (4-4-2): Manninger, Vivas, Luzhny, Weston (45), Upson, Silvinho; Black (Pennant, 73), Parlour (Cole, 89), Vernazza, Malz; Suker, Henry. Substitutes not used: Lukic (gk), McGovern.
Referee: M Liley (Leeds).
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