Advantage Minsk after a disappointing defeat for City at the Brandywell on Thursday evening.
An early goal from Galovic at the back post gave the Belarusian side the lead and set Derry on the back foot from the off.
In the action leading to the goal, Rory Hale took a ball to the face and was forced off, to be replaced by his brother Ronan.
The Candystripes began to settle into the game and press but any attempts to threaten the Minsk goal were thwarted.
City’s best chance in the first half came when sub Ronan Hale met a Jamie McDonagh cross with an overhead kick but the effort flew just wide of the goal.
Early in the second half, a good McDermott run up the line resulted in a cross which just brushed Ronan Hale’s head in what should’ve been a goal.
Dinamo continued the search for another goal to kill the game off and almost found one when Saroka’s effort slipped under Ger Doherty but the City shotstopper managed to scramble back to smother it on the line.
The goal was soon to follow though as Khvashchynski put away a squared ball that City looked helpless to stop.
McDermott got his marching orders late in the game for a second bookable offence as the game petered out with the Belarusians content with the result.
The away leg in Minsk is next Thursday 19th July with a 4pm kick-off (6pm in Belarus).
Photos: Event Images & Video