Tensions threatened to boil over at the Bahrain Grand Prix when Perez made contact with Button's car during the race, but Whitmarsh has played down suggestions of a feud.
"I have spoken to Jenson now and the thing is he is so mature in his attitude. That is the good thing about Jenson. He can stand back and be reflective in a way that you cannot when you are hot and sticky after just stepping out of the cockpit," Whitmarsh told AutoSport.
"Very quickly he gets to that point where, because he is an intelligent guy, he will know that Sergio is not a bad guy."
Red Bull driver Sebastian Vettel won the race.