Batsman Feroze Khushi, who was 12th man during the club's Bob Willis Trophy final win against Somerset, was photographed recoiling as beer was poured over him on the balcony at Lord's, reports Sky Sports.
Following the incident the club have admitted the celebrations failed to meet their inclusive values and pledged to do more in the future.
A spokesman for the club said: "Essex County Cricket Club prides themselves on their work within multi-diverse communities throughout the county and the surrounding areas.
"For a substantial period of time, Essex have had a multi-diverse team with players from different backgrounds, religions, and races, where cricket is at the heart of these communities.
"The club has worked extremely hard and will continue to bring cricket to anybody and everybody, and educate on diversity, but further work needs to be done across both sport and society in general, to widen people's knowledge and make them more aware of cultural differences."
Imam Ahmad Habib, the leader of Colchester Mosque in Priory Street, said further education was necessary in the UK on the cultural differences in relation to alcohol.
He said: "If someone is a devout Muslim it would considered impure and if the player involved is a practicing Muslim he has probably spent his whole life avoiding alcohol.
"Even the smell can be off putting for some as they have grown up staying away from it.
"Muslims often avoid going to pubs or even restaurants to avoid being near alcohol.
"There needs to be more education around the issue in Britain certainly.
"With alcohol, often people do not realise there are people who avoid it completely. There needs to be more education on that generally.
"It would also be good to have a discussion about these celebrations in sport and whether there is a more inclusive way of doing them."
Essex reasserted their status as English cricket's red-ball standard bearers by claiming the inaugural Bob Willis Trophy after a five-day draw was settled on first-innings runs.
The Chelmsford side are the reigning county champions, having also taken the honour in 2017, and now have a third red-ball title in four years.
Although 21-year-old Khushi did not feature in the final, he made four appearances during the group stage.
After England's Cricket World Cup victory last year, other squad members waited for Muslims Moeen Ali and Adil Rashid to step away before spraying Champagne.