The Blues manager expects to see his team strive for higher standards of behaviour in the public domain following the fall-out of John Terry's four-match ban for racial abuse
The club's positive start to the season has been overshadowed by the four-match ban and fine handed out to captain John Terry for racially abusing Anton Ferdinand last season.
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Di Matteo confirmed that Cole will be punished for his outburst in accordance with the Blues' social media policy and called on his players to respect the rules the club have laid down to create a healthier atmosphere around Stamford Bridge.
"I come from Switzerland, I like rules," he told reporters. "They are there to be respected. I wouldn't say I'm a disciplinarian but you need rules to be able to live and work together.
"The image of the club is very important to us. We have rules and if anybody breaks them there is disciplinary action taken against them.
"We have standards. We strive to have high standards. Hopefully going forward we can be better in showing those."