Greek striker Georgios Samaras, who started on the left of midfield with Bernardo Corradi and Darius Vassell, scored the game's only goal in the 35th minute.
Sylvain Distin was ruled out with a groin strain while Micah Richards had a hip injury but both are expected to be fit for Sunday's game against Kashima Antlers.
Left-back Stephen Jordan therefore filled in at centre-back alongside new captain Richard Dunne.
Corradi had 2 first half headers from Trevor Sinclair crosses but the first went narrowly wide and the second was tipped wide by the keeper.
City's new Italian striker did well on the right to cross for Samaras, who fired home with his left foot at the far post.
The second half saw an official stop Antoine Sibierski from coming on because he was wearing a wristband!! Ben Thatcher was then harshly shown a second yellow card with 12 minutes left.
The home side's best opening came with 8 mins left when former Germany and Bayern Munich striker Carsten Jancker failed to connect with a pass from just 6 yards out.
Manager Stuart Pearce was dismayed by the Sibierski incident but was overall pleased with the side's showing.
"It's a bit of a mystery why that happened because Antoine was wearing the wristband that about 7 of Shanghai's players were also wearing out on the pitch. I'm sure it will all be resolved before Sunday," he told the City website.
"We played at a high tempo, it was a good test and overall the match was a good examination for us. Obviously it was not ideal to go down to 10 men."
City: Weaver, D Mills, Dunne (c), Jordan, Thatcher, Sinclair, Barton, Hamann (Reyna), Vassell (Dickov), Samaras, Corradi.
Unused Subs: James, Hart, Sibierski, Miller.