The Italian coach was sacked after a 3-0 defeat to Juventus effectively ended the club's hopes of defending the Champions League crown, and the Spaniard has been put in place until the end of the season.
While the 52-year-old has seen 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, trying to play good football, trying to win games," he told reporters. "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 leader Manchester United with a game in hand, and Benitez feels the fans must side with him if the team is to mount a title challenge.
"I hope they will realize that I will try to do the best for the club," he said of the fans. "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."