Wilson benefited from having another forward alongside him and met Andreas Pereira's cross with a firm close-range header to level the scores with 14 minutes remaining.
However, back came the home side and Pearson had to make a good block when Gollini pushed away a cross before Shakhtar were rewarded for some pressure when Ioannou's backheel led to problems in the defence and Zubkov found the bottom corner after Gollini had initially saved well.
There will still be plenty of positives for Butt to take from the game, particularly with the dominant second-half display on foreign territory.
United: Gollini; Evans (Fletcher 63), Grimshaw, Ioannou, Goss; Weir, Rothwell, Pearson, Pereira, Byrne (Harrop 14); Wilson. Subs not used: Henderson, Rowley, McConnell, Willock, Barber.