The Spaniard has succeeded the sacked Roberto Di Matteo on an interim basis and his former connection with Liverpool has made him unpopular in London.
Sections of the Chelsea support held up banners against Benitez and they also stood and applauded in the 16th minute, which was Di Matteo’s shirt number in his playing days, before the game ended in a forgettable 0-0 draw.
Sergio Aguero wasted the best chance of a turgid Premier League encounter in driving rain, which the visitors had the better of in the first half but the home side the second.
The draw moved unbeaten champions City to within a point of new leaders Manchester United, leaving Chelsea fourth.
Benitez has shored up the Blues’ defence during his four days in charge but he has his work cut out to get them playing the scintillating football demanded by the watching Roman Abramovich – and to get Fernando Torres scoring.
But that is nothing compared to winning over the fans on today’s evidence.
Chelsea’s stadium announcer was drowned out by jeers as he appealed for calm in order to pay tribute to former Chelsea boss Dave Sexton, whose death was confirmed on Sunday.
There were also expletive-laden chants of “you’re not wanted here”, and signs reading ‘Benitez out’ – coupled with songs and banners hailing the sacked Di Matteo.
The off-field action was of more interest than events on the pitch, where, although Chelsea kept a first clean sheet in 11 games, they never truly looked like scoring.
Torres, who worked with Benitez at Liverpool, was closely marked by City captain Vincent Kompany and the Spaniard again appeared shadow of his former self.