City lost their second consecutive away game after goals from Danny Murphy and Grant Hanley for Rovers.
Murphy intercepted a poor Mark Wilson pass and strode forward before unleashing a 25-yard drive that Tom Heaton got a hand to but could not keep out while Hanley got ahead of Greg Cunningham to stab home Blackburn's second.
"It didn't feel like a proper cup tie. It was strange, and I felt that we've gifted Blackburn both goals but certainly the first goal is crucial," McInnes said.
"We give the ball away in an area we know we have to handle the ball well because Blackburn are a counter-attacking team, and want to get you on the back foot.
"Certainly the goal they scored from, we should be dealing with. I felt second half, we made changes to freshen things up.
"We brought three substitutes on quite early but we lose a second goal from the second part of a set play and that's another gift. It's a messy goal. I don't think Blackburn have had to work too hard for both of their goals."