The organisation's chairman warns the club is in "turmoil" and that, while they "appreciate" what Roman Abramovich has given to the Blues, the Spaniard is the wrong man for the job
The former Liverpool boss was put in charge at Stamford Bridge back in November after Roberto Di Matteo was relieved of his post, just six months after winning the Champions League.
Many followers of the west London outfit have refused to get behind the new manager, though, and instead continue to chant "there's only one Di Matteo" after the 16th minute of matches, representing the number he wore at the club.
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Trizia Fiorellino told The Daily Mail: "We are in turmoil and there is a danger we will lose the soul of the club.
"I know of fans who will not watch Chelsea until Rafa Benitez has gone. In my experience, fans who stop watching the club don’t come back."
Blues chairman Bruce Buck also received abuse when taking to the Stamford Bridge pitch before the clash, which saw £50 million man Fernando Torres record another below-par display.
Fiorellino suggested that the club should have guessed how fans would react to Buck's appearance, while he stated they are thankful for the owners' money but they strongly disagree with a number of decisions they have made.
"The booing of Bruce Buck was universal and vitriolic," he continued. "It was a serious miscalculation by someone at the club to let him on the pitch before the game.
"We are fully appreciative of everything Roman Abramovich has done for the club but Benitez is not the right fit for Chelsea.
"He was brought in to get the best out of Fernando Torres, but if anything the body language has become even worse. There is a lot of disharmony among the supporters about everything that is happening and it is tearing the club apart."
Supporters also remain fiercely loyal to midfielder Frank Lampard, who is reportedly being forced out of the club at the end of the season by not having his contract renewed.
Fiorellino said of the move: "It is an unpopular decision to let Lampard leave and it seems John Terry may be next."