Di Matteo concedes Chelsea reputation has been battered
The sagas have arguably tainted the Blues like never before, with the former found guilty by the Football Association of racist abuse and the latter launching a foul-mouthed Twitter tirade against the English game's governing body.
Di Matteo said: "The image of the club is very important to us, of course.
"We have rules, and anybody who breaks the rules faces disciplinary action against them.
"We strive to have high standards and hopefully, going forward, we can be better at showing those."
Former Chelsea and Italy midfielder Di Matteo, who was born in Switzerland, added: "I come from Switzerland so I like rules, and rules are there to be respected.
"I wouldn't say I'm a disciplinarian but, when you live and work in a group environment, you need rules to be able to live together and work together."