Benitez was appointed as Everton’s new manager on a three-year contract last month, replacing Carlo Ancelotti, who left for Real Madrid.
The 61-year-old’s appointment was met with disapproval from some Everton fans, who threatened him with a banner to stay away from the club.
The former Valencia and Napoli manager previously spent six years in charge Everton’s Merseyside rivals Liverpool, winning the UEFA Champions League and FA Cup with the Reds but he irked the Toffees supporters in 2007 when he described the Goodison Park outfit as a ‘small club’.
Benitez insists his belittling of Everton is in the past as he looks forward to winning the club’s fans over.
"To be fair, the Evertonians around my place are quite happy and very supportive. Even the Liverpudlians accepted it was an opportunity for me to come back to the Premier League," Benitez said in his first Everton press conference on Wednesday.
"About the banners - we can talk about one, two people. You never know. It's better to think about positives, how a lot of people were encouraging me to do well.
"Football is quite emotional and everybody will have their opinions. For me it's a challenge, a chance to do well in the Premier League, and show everyone we can compete.
"I was convinced when I decided to say yes, or even decided to start talking. It's not something I'm scared of, it's the opposite. I want to win, I want to do well. That is to be competitive for me, to be ambitious."
Asked about making his ‘small club’ remarks, Benitez said: "It depends on the context. It was a long time ago. You are fighting for your club and that is what I will do now. I will fight for Everton.
"I will try to do my best every single game. I am really pleased this club is getting bigger and bigger."
