United fell behind in the 19th minute when Bojan capitalised on Memphis Depay’s error to put the hosts ahead at the Britannia Stadium.
The Potters then doubled their lead shortly after when Marko Arnautovic’s 25-yard strike beat David De Gea after Bojan’s free-kick had hit the wall.
United brought on captain Wayne Rooney and improved after the break but were unable to find the net as they slumped to their third successive Premier League defeat.
The result has heaped further pressure on under-fire United boss Louis van Gaal, with the Red Devils set to host Chelsea at Old Trafford on Monday night.
And Herrera used his personal Twitter account to issue a Manchester United rallying cry as they look to turn their stuttering form around in the coming days.
Tough times. Fighting and working hard is the only way…🔴 pic.twitter.com/p8MQwDIrSD
— Ander Herrera (@AnderHerrera) December 26, 2015
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