McInnes criticised the award of a second half penalty, which Scott Sinclair saw saved by Joe Lewis, and claimed match winner Ryan Christie should have been sent off for a second bookable offence.
Celtic won the match thanks to a solitary goal, scored by Christie in first-half stoppage time.
“The penalty decision didn’t do us any real harm but it wasn’t a penalty in the first place and if we didn’t have a goalie like Joe Lewis it would have been 2-0 and far more difficult,” said McInnes.
“It was clearly outside the box and I also felt there was another yellow card challenge from Ryan Christie when Dom Ball breaks. The ref said he played the ball when he clearly didn’t.
“You need a lot of things to go for you in a final and it might sound churlish but a couple of decisions were really harsh on my team today. I love Ryan Christie but it was another yellow card and the referee was in a brilliant position to see that and I don’t understand how he can say he played the ball.”
McInnes confirmed that winger Gary Mackay-Steven, taken off on a stretcher after a sickening clash of heads with Dedryck Boyata, had regained consciousness and was recovering in hospital.