First-half goals from Jeff Hendrick and Craig Bryson left hapless City with only two points to show from their last nine games at Ashton Gate, where they have not won since August.
And McInnes was unhappy with the way his side conceded the goals.
"It doesn't matter what formation you employ if you fail to defend crosses as we did for Derby's two goals," he said.
"We also have a problem at the moment with being vulnerable after we concede.
"By taking their chances, Derby earned the right to get 11 men behind the ball in the second half and that made it very difficult for us.
"If we had taken our chances it would have been a different story. Liam Fontaine and Sam Baldock should have scored and there were other opportunities."