Ian Ross, Everton's Head of PR, issued a statement in response.
He said: "Whilst we would never condone the singling out of individual players for vitriolic insults, it is a shame that Mr Benitez chose to ignore the actions of his own club's supporters.
"Not only was Joleon Lescott subjected to an afternoon-long barrage of quite disgusting and quite audible abuse, Phil Neville was seemingly spat at several times and was also punched in the back by a supporter as he took a throw-in.
"We have asked Merseyside Police and our Safety Officer to look into the matter.
"In calling for Everton supporters to respect his players, Mr Benitez should, perhaps, remember his comments of 12 months ago when he sought to belittle one of world sport's oldest and most respected institutions by describing us as a 'small club'. Respect is a two-way street."