Kenny Miller was allowed to kick the ball out of Tuffey's hands for the opening goal in the 19th minute but there was little he could do when James McArthur curled high into the net in the 32nd minute.
Celtic's Kris Commons hit the third goal in the 51st minute.
A few City fans were in Copenhagen to see England beat Denmark 2-1. Aston Villa's Darren Bent and Ashley Young got the goals.
Picture copyright of Covsupport News Service. Credit CNS/DW