Cosgrove's case will now be heard by a Scottish Football Association fast-track disciplinary panel hearing on Tuesday.
And McInnes is expecting to have the Englishman available for his side's Boxing Day clash with Livingston at Pittodrie.
He said: "I'm hopeful that we've a chance to right a wrong with Sam's red card. As I said, for me it's never a red card.
"I'm not considering being without Sam on Thursday and hopefully common sense will prevail. Livingston are on a very good run and we'll have a job on our hands for sure."