The incident took place as players, officials and staff made their way up the tunnel at half-time after the visitors had come from behind to lead in the Premiership clash.
The start to the second half was delayed as ground staff cleared glass from a broken bottle in Celtic goalkeeper Joe Hart’s penalty area.
A Celtic spokesman said: “A member of our backroom staff was struck by a glass bottle. He required urgent medical treatment and stitches to a head wound. The matter is now in the hands of Police Scotland.”
Postecoglou said: “I think he is okay, he had a couple of stitches. It is disappointing because this is a fixture that gets beamed around the world, and stands on its own. Two teams going at it, first and second spot. You don’t need a couple of idiots ruining it.”
Cameron Carter-Vickers put the visitors ahead after Hoops midfielder Tom Rogic had cancelled out Aaron Ramsey’s opener.
Celtic’s win took them six points clear at the top, with six matches left to play.
Postecoglou was sad the action on the pitch was overshadowed.
“It is disappointing,” the former Australia boss said. “I thought it was a proper derby, the atmosphere was unbelievable, both teams were up for it, both teams were going for it.
“You don’t need it. I don’t know what people are trying to achieve by doing that.
“I thought it was a fantastic spectacle.
“Sitting here now as the winning coach, that kind of taints my view of it, but I thought anybody watching would agree it was a good game of football and you could tell there was something meaningful at the end of it by the way both sets of players went at it.
“Their crowd was up for it, our 700 was up for it and couldn’t stop signing. That is what you want.”
Gers boss Giovanni van Bronckhorst said of the delay: “It’s never good that due to situations the game has to be stopped. I don’t think it’s a good thing. Safety is first and I understand we have to wait for the pitch to be playable for both teams.”