It was far from the convincing performance that manager Sir Alex Ferguson had asked of his players as their Turkish opponents twice hit the woodwork and failed with two very strong penalty claims.
United also missed a penalty for the third consecutive game, with Nani failing with a second half effort which would have brought United some much-needed breathing space.
However, after their embarrassing group-stage elimination last season, this was at least a step in the right direction.
England midfielder Carrick struck after only seven minutes, appearing at the end of a magnificent, flowing move that also involved Robin van Persie and Shinji Kagawa before rounding goalkeeper Fernando Muslera to slot into the empty net.
United could count themselves fortunate to be in that position, however, as the Turkish visitors had a strong penalty appeal turned down inside the opening minute when Nemanja Vidic appeared to bring down Umut Bulut, although experienced German referee Wolfgang Stark rejected the appeals.
The incident left Bulut nursing an injury, the forward limping off after 15 minutes to be replaced by the former Bolton striker Johan Elmander.
But Galatasaray were a constant menace to the United defence, with Nordin Amrabat capping a lightning fast counter-attack with an 18-yard shot that clipped the top of the crossbar, before Felipe Melo came close with a header from a set-piece.
At the other end, Muslera saved early at the feet of Nani, a Paul Scholes shot almost fell kindly for Kagawa and Antonio Valencia's wicked cross was palmed away by the goalkeeper.
Selcuk Inan then pulled a free-kick back to the edge of the area for Hamit Altintop, who delivered a powerful strike which clipped the outside of the post.
United continued to live dangerously until the half-time whistle with Carrick tackling Altintop from behind just inside the area, as television replays once more suggested the home side were lucky not to concede a penalty.
But the hosts were then presented with the perfect opportunity to take a stranglehold on the game six minutes into the second half when Rafael collected a Paul Scholes pass, darted into the area and was brought down down by Burat Yilmaz.
Incredibly, following on from the examples of Robin van Persie and Javier Hernandez, who each missed a spot-kick in United's last two games, Nani stuttered in his run-up and saw an unconvincing penalty attempt comfortably saved by Muslera, diving to his right.
The miss could have proved even more costly, five minutes later, when Inan headed a cross from the impressive Altintop beyond David de Gea's dive and narrowly past the far post.
United were living dangerously and Galatasary missed another glorious chance to claim the equaliser their play merited on 71 minutes when Emre Colak found Burak Yilmaz on the break and the latter's shot was well saved by de Gea, who also kept out Colak's follow-up.
United brought on Darren Fletcher, the Scotland international who has been sidelined since November 2011 with a bowel disease, as a substitute to a rousing Old Trafford reception, although it was another replacement, Hernandez, who could have doubled their lead as he placed a Nani through ball well wide and into the side-netting.
Source: AFP
Source: AFP