At times during that difficult campaign eight years ago, it seemed United were headed for oblivion.
Within the space of three weeks Roy Keane was booted out by Alex Ferguson, sponsors Vodafone quit their shirt sponsorship deal two years early and United crashed out of the Champions League at the group stage.
Against the backdrop of a fans revolt in the aftermath of the Glazer family’s controversial takeover that had been completed just a few months before, it seemed United’s time at the top of the English game was over.
However, although they were well off the pace being set by eventual champions Chelsea, United finished the season with a flourish, bouncing back from a 4-3 defeat at Blackburn by winning 11 of their final 14 games to clinch second spot.
With Patrice Evra and Nemanja Vidic settling in and the Carling Cup secured too, the Red Devils had built enough momentum to ride over the storm created by Ruud van Nistelrooy’s exit and went on to enjoy one of the best three-year spells of their entire history.
Fletcher was part of the squad that won a hat-trick of titles, lifted the Champions League, played in another final and a semi-final, and also collected the League Cup and figured in the new Wembley’s first FA Cup final.
And that is what he is reminding United’s current youngsters of now.
“It is like 2006,” he said.
“Seasons can be turned on one result, one cup win, one massive performance. This can be the catalyst for future success.
“We have got to reflect on that and realise it has been done before.
“In 2006 we finished the season on a high. That carried onto the next season because that is the standard that we have set, that is what we know we are capable of. There is no doubt about it, we need to get back to that. The goal is always to respond and be successful. If we can finish the season on a high, get as high as possible in the league and go far in the Champions League then who knows what can happen.”
Given United, who host struggling Fulham on Sunday, have lost to Stoke, been dumped out of the Capital One Cup by Sunderland and were beaten by Swansea at Old Trafford in the FA Cup already in 2014, lifting the biggest trophy of all seems somewhat fanciful.
Yet Chelsea and Liverpool have all managed it from outside the top four.
Liverpool lost an incredible 14 times in 2004-05, finishing level on points with Bolton and ending the campaign 37 points adrift of champions Chelsea.
The Stamford Bridge outfit were not quite as bad seven years later, however, they could do no better than sixth in the Premier League following a dismal season that included Andre Villas-Boas’ dismissal.
So, if they can do it, why not United?
“We have got a tough tie against Olympiakos but if you get through that then we would be in the quarter-final,” Fletcher said.
“Then there would be only eight teams left. Our form has been good in the Champions League, so if we can carry that on and achieve a bit of success, it will set us up for next season.”
Meanwhile, Fletcher’s United team-mate Shinji Kagawa admits he has been “very irritated” by his own form this season.
United had high hopes for Kagawa when they signed him from Borussia Dortmund two years ago, but the Japanese has struggled to hold down a place in the starting XI.
Kagawa showed glimpses of his potential last term — like when he scored a hat-trick against Norwich — but he is yet to find the net this season.
The 24-year-old has completed just two Premier League games and he concedes he must improve.
“I still haven’t scored any goals this season so I’ve felt very irritated,” Kagawa said. “This is the first time in my career that I haven’t been able to produce so it’s disappointing.”
Juan Mata’s arrival at Old Trafford is likely to decrease Kagawa’s chances of first-team football, and Kagawa’s confidence appears to be very low.
“I pressure myself to score in every game but some days it feels like I just can’t win. I know I have to overcome that,” he added.
“Actually, if I can’t it really shows that I haven’t grown as a player. So because of that I have to really focus on the second half of the season and overcome that mental block.”