Jambos goalkeeper Zdenek Zlamal appeared to be struck by a visiting fan as he went to retrieve the ball, while Hibs head coach Neil Lennon was hit by a coin thrown from the main stand as he celebrated a Hearts goal being chalked off.
A 25-year-old man was also arrested and charged after an alleged assault on an assistant referee, while there were reports of missiles, including coins and flares, being thrown from the stands.
The statement read: “The two clubs are united in their condemnation of the isolated events which marred an otherwise compelling fixture, and will together work with Police Scotland to ensure those individuals concerned are identified and face appropriate sanctions.”
The SPFL has already issued a statement vowing to work closely with both clubs as well as the police in a bid to identify those responsible for any disorder at the Ladbrokes Premiership clash.
Hearts owner Ann Budge added: “The first thing I want to say is that we 100 per cent condemn the handful of unsavoury incidents that took place during last night’s Edinburgh Derby.
“We will work closely with Police Scotland and Hibernian to identify the individuals involved in these incidents to ensure they are banned from attending our two stadiums and are formally charged.
“While we condemn such behaviour, we must not fall into the trap of condemning the thousands of genuine football fans, who come to be entertained and who do nothing more than passionately support their respective teams.”
Budge revealed that, of the five arrests made on the night, one was made possible “because fellow supporters identified the culprits”.
She continued: “By working together in this manner we will succeed in removing the tiny percentage of fans, whose behaviour spoils things for the majority.
“Thank you to the thousands of supporters, from both teams, who created a fantastic atmosphere last night.”
Hibs chief executive Leeann Dempster echoed Budge’s remarks, adding: “The two clubs are united. This kind of behaviour is simply not acceptable.
“We do everything we can to ensure that we run matches in a way that is safe for everyone involved. Players, coaches, supporters, the media, everyone who goes to a football match is entitled to enjoy the match in safety and security.
“We will not allow the mindless actions of a few foolish individuals to jeopardise that.”
Dempster also called on supporters to come forward if they had any information concerning the individuals behind what she called “unacceptable and potentially dangerous behaviour”.
She added: “The two clubs work together in all kinds of ways, and there is great mutual respect. “There is an intense sporting rivalry, and we all enjoy that and would not wish to dilute it, but it needs to be a respectful rivalry.”