The interim manager believes he can prove his critics in the stands wrong and lead the west London club to success with attractive wins such as the 8-0 thrashing of Aston Villa
The Italian coach was sacked after a 3-0 defeat to Juventus effectively ended the clubs's hopes of defending their Champions League crown, and the Spaniard has been put in place until the end of the season.
While the 52-year-old has been subject to a backlash in the stands at every home game, he feels results such as the 8-0 win over Aston Villa will begin to convince fans he is the right man for the job.
"I said at the beginning, and I will maybe say the same at the end: my job is trying to bring the best out of players," he told reporters.
"Trying to play good football, trying to win games. And I am sure that the fans will appreciate this, and I think we will win together. So it is a question of time."
The Blues are 11 points behind Premier League leaders Manchester United with a game in hand, and Benitez feels the fans must side with him if they are to mount a title challenge, as they are all in it together.
He added: "I hope they will realise that I will try to do the best for the club. At the end of the day: it is the best for them. They will enjoy.
"I always say, the fans play every game with the manager: some players may or may not play, but the manager and the fans play every game."
The former Liverpool manager is still trying to build consistency with his preferred tactics, but feels he is on the right tracks with the trashing of Paul Lambert's side on Sunday.
He continued: "I always try to find the balance. The balance for me is to be strong in defence - like [against Villa], a clean sheet - but still attacking.
"I try to keep the team in good positions, good order; and after that - attacking.
"If you play at this level, you can carry on winning games. On Sunday, United drew [against Swansea]: these things can happen, but the problem, is if they happen to you. We have to be sure that we can keep at this level."
And the coach has warned his players they face a "top team" in Norwich on Boxing Day afternoon, with the Canaries flying high in 10th position in the league.
"Norwich were doing well: at the beginning they were under pressure, not too many good things; but after that they did well. They lost the other day, but still you can see that their team is professional and will be a top team," he added.