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 on Saturday.
The FA are awaiting referee Martin Atkinson's version of events in his official match report before deciding on what action, if any, to take.
Gotta lotta bottle: Bellamy had to duck the missiles at Goodison Park
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 the club's website.
Video evidence: The bottles rain down on Bellamy as he waits to take a corner
'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 per cent of our fan base.'
Taking action: Everton will come down hard on those found guilty
?Everton appeal Rodwell's controversial red card in Merseyside derby defeatBellamy faces objects of hate and Everton face an investigationDowning backs Carroll to take Liverpool by storm after derby delight All the latest Everton news, features and opinion All the latest Liverpool news, features and opinion Click here for the latest Premier League table, fixtures and results
Source: Daily Mail
Source: Daily Mail