Second half goals from Gary Teale, Neil Mellor and Clinton Morrison secured a 3-0 win that put the skids under Championship side City and gave the League One underdogs passage to the fourth round.
Millen admitted: "We were weak mentally after falling behind and the dressing room was too quiet afterwards.
"We looked a bad side in the second half and it showed we still have a lot of work to do over the rest of the season.
"It was a damaging result financially for the club and just how bad we will only know when we see who Wednesday draw in the next round.
"I have sent all my players home with a DVD of the match and will be looking for a response from them at our next training session."
Source: PA
Source: PA