The camera angles are not great but after seeing the action frozen it's clear that Bothroyd is not offside when the ball is played to him.
City were beaten by a third minute goal from Gabriel Agbonlahor, a cheeky back heel after a surging run from Carew. Cardiff competed though and created some decent chances with close range headers from Gyepes and Ledley and a couple of on target effiorts from distance from Whittingham and Burke.
Bothroyd saw one effort from a tight angle ricochet off the foot of the post.
Villa missed a 2nd half penalty after a fould by Gyepes but Milner saw him rocket shot come back off the post.
So no disgrace in losing to one of the top 6 sides in the Premier League but it's annoying that a bad decision has robbed us of a chance of extra time and a possible giant killing.
City are straight back into League action with a trip to Hillsborough on Saturday to face Darren Purses's Sheffield Wednesday.