Rooney has courted controversy this season with a series of incidents, including swearing into a camera and appearing to display a v-sign at Chelsea fans.
This week he also became embroiled in a row with a fan on Twitter, who he offered to fight after receiving an abusive message.
Losing his rag: Wayne Rooney offered to find a fan on Twitter after he received an abusive message from him
Cole, who scored 93 goals in 195 appearances for United between 1995 to 2001, believes Rooney needs to adjust his behaviour as the abuse comes with the territory.
'In football you'll always gets dogs abuse,' he said. 'If you're successful and are playing for the most successful team in the country, you'll get abuse.
'You must take that on the chin, play like he has done at the back end of the season and say judge me on the way I play.
'We're all feisty and get involved in the game. At times he just needs to taper it down a bit.
'We all get excited, want to play well and score goals. But some times we do need to taper it down. He apologises for doing it, then he gets caught doing it again.
On target: Cole says Rooney should stick to what he does best and score goals like this one against Blackburn
'I loved scoring goals but it wasn't for me to eff and blind after scoring. Scoring was one of the biggest thrills and when you do score you want to celebrate with your team-mates and fans, not throw verbals at people.'
Cole feels Rooney he would benefit from following David Beckham's example.
'Take a look at David Beckham - he received dogs abuse when he came back from the 1998 World Cup,' he said.
'But look at the way he turned it around - he got his head down, grafted, played some good football and is now the apple of everyone's eye in England.
'Who heads up the Olympic bid? David Beckham. Who heads up the World Cup bid? David Beckham. That's how you can turn it around.'
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