The Dons keeper was given a straight red card by referee Calum Murray on the stroke of half-time for whipping the feet from Georgios Samaras as the Celtic striker rounded him in the box.
Kris Commons sunk the resulting penalty past substitute stopper Nicky Weaver to give Celtic the lead, and the visitors wrapped up the win three minutes from time through James Forrest.
McInnes said: "I was disappointed that Samaras gets the chance to go through on goal but the referee called it right. There was definite contact there, the referee's made the right decision.
"There wasn't a lot in the game first half and I thought we could get something from the game but at 10 men in the second half there was only one team in it. They're a good team and they had an element of control, 11 against 10.
"The second goal was freakish, you'll never see another goal like it this season. I think 2-0 was hard on us but we'll pick ourselves up."
Celtic boss Neil Lennon concurred with his Aberdeen counterpart's assessment of the penalty decision and subsequent sending off.
Lennon said: "I thought it was clear penalty. The goalkeeper's unfortunate, it's the law and it's very, very tough at times."