The three-times winners and 2011 finalists failed to reach the knockout rounds last season - the first time since 2005/06 they had fallen at the group stage - and they won just one game at home in a dismal campaign.
Their undoing, acknowledged with rare candour by Sir Alex Ferguson, had been complacency and a vulnerability in defence at Old Trafford that cost them dear in a 3-3 draw with Basle and a 2-2 draw with Benfica.
So Ferguson's overriding emotion after Michael Carrick's winner on Wednesday was one of relief at the result rather than concern at the performance.
"Three points in the opening game are very important, especially when you look at what happened to us last season," Ferguson, who celebrated his 100th Champions League win, told reporters.
"In the first half we gave the ball away too often and they counter-attacked really well. In the second half, we were much more solid at the back, and all the chances fell to us.
"It was a good opening game, they were very confident in their possession, and missing the chances we did in the second half we kept ourselves on the edge."
The Scot might revise his thinking when he reflects on the bigger picture.
United were poor in possession, lacking control in midfield, unable to conjure a clear chance for Robin van Persie, and reliant on good fortune and the fingertips of David de Gea in safeguarding their lead.
Indeed, Galatasaray, returning to Europe's elite club competition for the first time in six years, must be wondering how they failed to repeat the achievements of Basle and Benfica.
The Turkish champions hit the woodwork three times, through Nordin Amrabat, Hamit Altintop and Selcuk Inan, and had one strong penalty claim turned down.
Nani's penalty miss for United - his feeble 53rd-minute spot-kick was saved low by Fernando Muslera - merely compounded his team's struggle.
INCISIVE PASSES
Their jitters had been evident as early as the first minute.
Captain Nemanja Vidic was slow to react under pressure from Umut Bulut, but even though the Serbian defender appeared to trip the Galatasaray striker, referee Wolfgang Stark waved play on.
Carrick's seventh-minute breakthrough, his first Champions League goal in three years, was well worked and hinted at better things for the home side.
The England international exchanged incisive passes with Van Persie and Shinji Kagawa before taking on Muslera in a one-on-one, but even though the keeper clipped Carrick's heels, the midfielder kept his composure as he lost his balance to slide home the finish.
"I don't get many, so when the chance is there," Carrick told Sky Sports. "You can go down, and there's a chance the keeper will be sent off, but we've missed three penalties now [this season], so taking the chance was the right one."
The goal did nothing to deter the visitors.
Galatasaray, working with a bold formation from coach Fatih Terim of two up front, forced United backwards and twice before the break went close to an equaliser.
Amrabat cut in from the left and bent a curling right-foot shot from 25 metres on to David de Gea's crossbar, and Altintop, the former Bayern Munich midfielder, ripped a low shot on to the base of the post.
Terim's side struck wood for the third time in the 56th minute when Inan flicked a header on to the outside of De Gea's right-hand upright.
By then Nani had blundered from 12 metres.
Right-back Rafael won the penalty, drawing a foul from Burak Yilmaz as he burst into the area, but the Portuguese stuttered in his run-up and his effort was easily saved by Muslera.
Galat
