Around 60 seats in the East Stand, where the Posh fans were housed, were broken at the game on Saturday - which the visitors won 2-1 thanks to a couple of late goals from Britt Assombalonga and Tommy Rowe.
Peterborough have requested evidence from CCTV and appealed for any footage from social media to help charge those responsible, with chairman Darragh MacAnthony vowing to ban anyone who is found guilty.
A statement on Peterborough's official website, theposh.com, said: "Following the destruction of areas of seating in the away seated area at the Matchroom Stadium by a very small minority of people in the stand, the football club have apologised for this disgraceful and sad behaviour and have offered to pay all reinstatement and labour costs.
"The football club have also asked for all photographic and CCTV evidence relating to the incident whereby any guilty party will be charged with criminal damage and prosecuted."
MacAnthony called the incident 'embarrassing' via his Twitter account before going on to add: "As promised, we have worked with Leyton Orient on the damage caused by a few idiots, and I will cover the cost of repairs.
"I, of course, apologise on behalf of my club, and we are currently working to identify those responsible so they can be prosecuted for criminal damage and banned from coming to games again for tarnishing the club's image."
- Crime & Justice
- Society & Culture
- Britt Assombalonga
- Darragh MacAnthony