Steven Davies cancelled out Sone Aluko's early strike but an own goal from Cole Skuse earned the visitors three points - and left McInnes's men in the drop zone.
"We have a sickness bug sweeping the club and more than one player went out there feeling under the weather," McInnes said.
"Stephen McManus complained of illness, but we are short of centre-backs so he had to play, and Steven Davies was sick at half-time.
"We are on a bad run and the only remedy is hard work. But I have 100 per cent faith in the players here and I know we are capable of digging ourselves out of trouble.
"We have to keep believing and that applies to the fans too. It is hard at times like these, but I am convinced we have the squad to turn things around.
"It won't happen overnight, but there is no shortage of commitment from players or staff."