The Australian team publicly criticised England for their negative tactics during the fifth test and coach Darren Lehmann also fired a shot at fast bowler Broad that earned him a fine.
Cook said the bagging of his team by Australia wouldn't faze his side.
They were now turning their attention to the first test in Brisbane in three months.
"It's water off a duck's back," Cook said.
"You can say what you want. The guys in the other side are entitled to their opinion.
"What is important to us is how we go about things and how we perform."
England and Australia were at each other verbally all series, with tensions spilling over at various times in the fifth test.
When asked whether England had sledged Australia more this series than in earlier series, Cook didn't deny that was the case.
However, he said things did not get out of hand.
"It's been an interesting series in that way," he said.
"It's been played in the right spirit. It's been hard, tough cricket and no side has been prepared to give an inch. Maybe because it's so recent you forget what happened in 2011, 2009 and 2007."
Despite Australian coach Lehmann encouraging home fans to "give it to" controversial non-walker Broad, Cook was confident England would be well received by Australian crowds.
"The last time we went there I thought the atmosphere was fantastic," he said.
"When we have played well they have treated us with respect and I don't think it will be any different."
Australian captain Michael Clarke denied ill-will between the teams and said he would be having a beer with England players post-match.
Clarke was involved in a slanging match with Pietersen on day three at The Oval but insisted the series had been played hard but fair.
Cook defended the fact his team scored at just two runs an over on day three, but five on the final day.
He said Clarke deserved "a little bit of credit" for a bold declaration that gave England a target of 227 from 44 overs to win in the final session.
In the end bad light stopped play and forced a draw with England 21 runs shy with four overs left.
- AAP