You would have to put them on the rack before they might admit it, but amid the obviously sincere disappointment expressed by Manchester United's staff and players at the ending of their run of 29 matches unbeaten in the league, there may also have been just the faintest sense of relief.
How else to explain the lack of urgency, let alone desperation, as they chased the game on a wild and wet Wolverhampton evening? Shorn of the comforting presence of Rio Ferdinand, who suffered a calf injury in the warm-up, and faced by a Wolves side buoyed by the knowledge it had already beaten Liverpool, Chelsea, Manchester City and Sunderland, United, having gone ahead with an early Nani strike which beat Wayne Hennessey at his near post, barely created a chance worthy of the name throughout the entire second period.
For Alex Ferguson to take defeat as well as he apparently did suggested the Scot himself may have become aware that the need to avoid defeat had, unconsciously or otherwise, begun to inhibit his players. Not, as Mick McCarthy pointed out, that it prevented Ferguson informing his opposite number that he had been "a lucky so and so".
"Actually, he didn't say 'so and so', he said something else," grinned the Yorkshireman. "And I said, 'Great, I'm delighted you're saying that,' because I've waited years and years and years to be called a lucky so and so by Alex. But he said it with his tongue in his cheek and a smile on his face and said we'd earned it."
So they did, with a performance of such defensive energy and commitment that it must drive McCarthy quietly bonkers. How, he was asked, could a side which has now beaten five of the Premier League's top seven sides still be bottom of the league? There was a certain dry humour in his response – "Because we've been bobbins against the teams around us" – but no one at Molineux will be laughing if a squad of players which can beat the best goes down because it cannot summon up the collective will-power to play with similar determination against lesser sides.
Whether they will make it six out of the top seven by beating Arsenal on Saturday remains to be seen, but United, as Darren Fletcher pointed out, can concentrate on preparing for a potentially crucial Manchester derby.
"Maybe people will stop talking about the run now," said the midfielder. "The main thing for us is to win the league, not to stay unbeaten. We could have remained unbeaten all season and not won the league: what point would that have made?
"Now we will have to show character, and we have a great opportunity because matches don't come much bigger than the Manchester derby. We will be ready for that game."
Roberto Mancini's team will need to be wary because Fletcher's words sounded as much like a threat as a promise, but with Ferdinand already out, Ferguson will be hoping there is no further fallout from the this week's internationals.
"To my mind [scheduling midweek internationals] is crazy but we have to get on with it," he told a television interviewer. "We have plenty of players who are not involved in international games and they will all play next week. We have to give consideration to the ones who are travelling, have to play, and then come back for the City game on Saturday lunchtime."
That United missed Ferdinand was unquestionable, though the blame for the goals powerfully headed home by George Elokobi, and fortunately deflected in by Kevin Doyle, for once lay more at the door of captain Nemanja Vidic than Ferdinand's late stand-in Jonny Evans.
Yet to single out any United player for criticism would be unfair on a day when the collective failure was exemplified by the remarkable sight of Ryan Giggs, of all people, kicking out at Doyle as the Wolves striker cheekily attempted to waste a little time.
Had the referee seen it clearly Giggs would surely have received the first red card of his career, and it can only have been his saintly reputation which led to Doyle rather than the Welshman receiving an official ticking-off.
"I imagine if it had been a Wolves player challenging him it might have been different," said Doyle, nursing a bloodied nose and thick lip after getting an elbow in the face from Chris Smalling.
"To be fair, I was acting a bit of an idiot by hanging on to the ball, and he probably deserves a bit of leeway after the career he's had and all the games he's played. I wouldn't like to see him get done for it but it was strange me getting on the receiving end of the ref's tongue for it!"
Scorers: Wolves Elokobi 10, Doyle 40. Manchester United Nani 3.
Subs: Wolves Foley (O'Hara, 59), Ward (Hammill, 64), Ebanks-Blake (Milijas, 88). Unused Hahnemann (gk), Craddock, Edwards, Fletcher.
Man Utd Scholes (Carrick, 46), Smalling (Evans, 65), Hernandez (Berbatov, 65). Unused Kuszczak (gk), O'Shea, Anderson, Owen. Booked: Wolves Henry, O'Hara Man Utd Scholes, Rooney.
Man of the match Elokobi Match rating: 6/10.
Possession Wolves 51% Man Utd 49%.
Attempts on target Wolves 5 Man Utd 7.
Referee M Oliver (Northumberland). Att 28,811.