The Spaniard has been named coach at Stamford Bridge until the end of the season following the departure of Roberto Di Matteo.
Benitez had a number of Champions League showdowns with Jose Mourinho's Chelsea, when the Liverpool manager and some of his comments at the time antagonised the Blues fans.
But he said at his unveiling on Thursday: "I want to be honest, if I say this or that, I have to analyse the context. We were playing against Chelsea in the semi-finals of the Champions League.
"If I am a fan I want to see the manager fighting for my club. I don't see this as a lack of respect for Chelsea's fans, just a manager defending his team.
"I like to do things in the right way for the fans. The fans and manager want to win every single game, nobody wants to win more than the fans and manager. At the end I think that they will be pleased."
Benitez said working for Roman Abramovich would be "easier" than for George Gillett and Tom Hicks at Liverpool, despite admitting he had never even spoken to the Chelsea owner.
Benitez's relationship with ousted Anfield chiefs Hicks and Gillett eventually led to his departure two years ago.
"I will meet him today," Benitez said of Abramovich after being unveiled as the Russian's ninth manager in just over eight years.
"The main thing is that I have spoken to Michael Emanalo, the technical director, and he's my link. I like to speak about football with him. That's my priority.
"If you have two bosses who aren't talking to each other [as I had at Liverpool], it's difficult.
"You want a striker and one of them says: 'I don't know...' This will be easier."
Benitez, who reportedly rejected the chance to become interim manager prior to Roberto Di Matteo's appointment in March, insisted he would be more than a stop-gap - saying he would target trophies in what could be a short spell as Blues boss.
"I don't care about the short-term, we have five trophies to fight for," he added.
"I've won everything you can win as a club manager (referring to Spanish Liga titles, Champions League and UEFA Cup). I have more hunger and desire to win trophies than before."