Objects - including what appeared to be at least one coin and a number of plastic bottles - were seen being hurled at the likes of Luis Suarez and Craig Bellamy at Goodison Park in the 216th Merseyside derby.
The Football Association are awaiting referee Martin Atkinson's version of events in his official match report before deciding on what action, if any, to take.
Everton are working closely with Merseyside Police to examine video footage from the match, in which the Toffees had Jack Rodwell controversially sent off and conceded second-half goals to Andy Carroll and Suarez.
"We are fully aware of the incidents which occurred during Saturday's derby game," club director of communications Ian Ross told Everton's website.
"We are currently working with Merseyside Police on collating and analysing all available CCTV footage of the incidents.
"If we can identify any supporter who threw anything - and we mean anything - on to the pitch on Saturday we will take immediate firm and far-reaching action.
"This behaviour is totally unacceptable and will be rightly condemned by all right-thinking Evertonians - and that is 99.9% of our fan base."
Source: Team Talk
Source: Team Talk