The ex-Liverpool boss accused the Blues board of making a "massive mistake" by labelling him as interim manager, and the Spaniard hit out against the fans for continuing to boo him following his side's 2-0 win over Middlesbrough in the FA Cup fifth round.
"My relationship with Roman is very good," Benitez told BBC Sport. "No, [I won't be sacked]. They know how we work and what we are trying to do. The players are really happy in what we are trying to do. Sometimes you win, sometimes you cannot.
"The atmosphere in the club is really good. There are no issues in the team. In terms of what we do, the players are fully behind the methods. If we stick together and support the players, we will be able to win games. Then at the end of the season I will leave and then they can criticise.
"I'm thinking about my team and my club. I want to win every game. I've tried to explain the way is to support the team in every single game. We were winning [against Middlesbrough] and still they were singing. I think that will not do our team any favours."
The 52-year-old moved to Stamford Bridge in November to replace sacked Roberto Di Matteo.