A number of disturbances took place during the 90 minutes with chairs being launched from the Rangers end and pyrotechnics being set off.
A 25-year-old male from Aberdeen had been charged for possession of a pyrotechnic with a 22-year-old male from Glasgow charged for offensive behaviour within a football stadium.
A probe has also been launched into vandalism of the Rangers team bus in the early hours of Sunday morning in the Deeside area.
On the pitch, James Maddison snatched a last minute 2 – 1 victory for the home side with a devastating free-kick.
Chief Superintendent Campbell Thomson said: “As anticipated the vast majority of fans who attended Pittodrie on Sunday acted in a safe and responsible manner which assisted officers in ensuring the safety of those in attendance and the wider public. I would like to take this opportunity to thank them for their support.
“In saying this, and despite repeated warnings from Police Scotland in the lead-up to match, I am extremely disappointed that a very small minority of fans chose to conduct themselves in an anti-social and completely unacceptable way. I understand that feelings run high at these events, however such behaviour is inexcusable. It also creates significant security issues which put your own safety and the safety of others at risk.
“For those who have committed offences and were not detected at the time I can assure you that you will face the consequences of your actions. Retrospective enquiries are being carried out and we have a dedicated team working in partnership with both clubs to identify those people in the stadium and outwith who let not only themselves down but their clubs too.
Anyone with any information should contact Police Scotland on 101 or Crimestoppers anonymously on 0800 555111.