The Chelsea Supporters' Group have asked the Spaniard to try and mend the bridge between he and the fans by saying he is sorry for negative comments he made about the Blues faithful and suggesting he would never want to managed the Southwest London club.
Benitez received a cold reception in his first game in charge at Stamford Bridge - Sunday's 0-0 draw with Manchester City - but he is not about to bow to fan pressure and apologise for something that occurred years ago.
"The problem is that we cannot analyse what I did nor what I say," said Benitez.
"We cannot really check. I will show them that I can try my best."
He added: "Imagine that you have a player that has no support of fans. What I will tell him is - listen, stay focused, work for your club. Don't be distracted, concentrate on football. I understand. I know about the fans.
"But at the same time I will try to prove that I am here for the right reasons, that I am here to win. I will concentrate on my coaching, to improve players, and to win."