The resentment stems from a fiery relationship between Liverpool and Chelsea when Benitez was at Anfield, with the Spaniard once saying he would never manage Chelsea and appearing to criticise Blues fans by saying they needed flags to get behind their team.
Trizia Fiorellino told Press Association Sport: "I think (an apology) would help for some fans. Even an acceptance of what was said would be a start."
The former Liverpool boss was greeted with a chorus of boos and banners calling for him to leave when he walked out onto the Stamford Bridge pitch for his first match in charge against Manchester City on Sunday.
Fiorellino added: "He's said he was trying to defend his club at the time but (then Chelsea boss Jose) Mourinho was the master of that and I don't think he ever directly ridiculed supporters of another club. It's quite a thing to try to undo but an acceptance could definitely bring some people back on board. I do think he's a tough sell, though."
Benitez was given a contract until the end of the season after the sacking last week of Roberto Di Matteo, who won the Champions League and FA Cup in May.
Di Matteo was also a hugely popular player at Stamford Bridge and Fiorellino even speculated that his departure in favour of Benitez may have been a message to the fans from owner Roman Abramovich.
"They don't listen to the fans," she said of the board. "I don't think Chelsea fans should be picking the manager or anything but it was pretty evident there were two people the supporters would not accept, and that was Avram Grant and Rafa Benitez.
"Some fans feel almost that it was a message to the fans to say, 'We pick who we want', almost spiteful."