Blues supporters called for their new manager to say sorry for what they perceive as criticism of them while he was in charge at Liverpool.
Benitez endured a savage reception upon his introduction as Chelsea boss in Sunday's Premier League draw against Manchester City and fan groups have suggested there will be no let up in tomorrow's west London derby with Fulham.
The chair of Chelsea Supporters' Group said an apology would help win over some fans but, as during his unveiling on Thursday, Benitez questioned the accuracy of some of the quotes attributed to him.
"The problem is we can analyse what I said and didn't say," he said. "We can't be checking if it's true or not. I'll try my best to win their trust. That's it."
Meanwhile, Benitez has admitted he does not know whether Fernando Torres can recapture his Liverpool form at Chelsea.
Interim Blues manager Benitez insisted he could improve the fortunes of Torres, who he helped become one of the best strikers in the world at Anfield and has flopped since his £50 million move to Stamford Bridge.
But Benitez acknowledged the 28-year-old was not the same player he had been before joining Chelsea and needed to improve physically to stand a chance of recapturing his glory days.
Three Blues managers have failed to get Torres scoring regularly, each repeatedly insisting there was nothing wrong with the forward.
The man who knows his fellow Spaniard better than any of them said: "He's not exactly the same player now, because he was at maximum level at this time [at Liverpool].
"But I think he can come back. How close? I don't know. It depends on the rest of the team. I'm sure he can improve, but the team has to help him."