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Duncan Ferguson wants his Everton players to "run themselves into the ground" and said recent performances have not been good enough.
They face Aston Villa on Saturday having lost nine of their past 12 Premier League games, dropping to 16th.
"They should roll up their sleeves and fight for the club in every single game," said the Scot.
Speaking to evertontv, Ferguson added: "They should give everything. They should run themselves into the ground.
"Imagine if you asked a fan to put a shirt on and get on the pitch, what would they do? Well they need to do that.
"I am getting among the players and telling a few home truths because the past has not been good enough."
Former Liverpool boss Benitez was sacked on Sunday after just seven months in charge following a 2-1 defeat at Norwich.
Ferguson has been placed in charge for "upcoming games" as the club begin its search for a sixth permanent manager in as many years.
It is Ferguson's second spell as caretaker manager after taking charge of four games in December 2019 following the dismissal of Marco Silva.
The first of those matches was a 3-1 win against Chelsea at a raucous Goodison Park, and Ferguson wants the fans to recreate that atmosphere when they take on Aston Villa.
"We are all willing for us to get a result on Saturday. It is a difficult time - results have been really poor, to be honest," added Ferguson, who scored 72 goals in 273 appearances for Everton across two spells between 1994 and 2006.
"It was an electric atmosphere [against Chelsea], one of the best I've experienced at Goodison, and I am sure they [the supporters] will be well, well up for it this weekend.
"We really need them to push us across the line for the whole game."
Ferguson also played down the prospect of taking the job full-time, with Wayne Rooney and Frank Lampard among the names being considered for the role.
"I'll only be in charge for the upcoming games. The club are in a process of going through their candidates," said Ferguson.
"They will go through that process and I am sure they will get the best man for the job."
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