Mitchell slams "mindless morons"
Both sets of players were taken off the field by referee Mike McCurry after violence involving both sets of fans erupted midway through the first half.
The trouble was sparked after Aberdeen striker Robbie Winters was struck by a coin thrown from the Rangers fans and police were called in to quell the trouble.
Mitchell revealed that a detailed investigation into events at the ground will take place on Monday to find out how the problem got out of control.
"We were particularly concerned about the potential for incidents at this game and, as a result, in the days leading up to the match, Iain Blair - our director of administration - was in contact repeatedly with the police and security advisors from both clubs," said Mitchell.
"We triple checked that all necessary steps had been taken on Friday afternoon.
"Despite the strenuous efforts of police, security staff and club officials, a mindless minority of morons engaged in behaviour which will sicken any true football fan.
"We utterly condemn the behaviour of the small minority in both sets of fans.
"Given this extremely regrettable incident, we will now be in contact with Grampian police and both clubs for a detailed debriefing on Monday morning.
"It may be, although it is too early to be certain, that future matches between Aberdeen and Rangers will be required to kick off in the early afternoon as is the case with Old Firm matches."
Meanwhile, Winters feels that referee McCurry had no alternative but to take the players off the pitch as their safety could not be guaranteed and that his head injury was not serious.
"I could just see coins flying by my head but the referee stopped it and said to try and get on with it," said Winters.
"But one eventually hit the back of my head but it had to be stopped because there was £10 worth of change out there. "It was not the sort of thing you want to see in Scottish football.
"I'm fine. I'm sure a pound coin would have caused a bit more damage but there is just a wee lump at the back of my head."
