A huge campaign on social media sprang up after details of the revised crest, which significantly removed the club's motto Nil Satis Nisi Optimum (Nothing but the best), were revealed over the weekend.
And while it is too late to change for next season, the club have pledged to consult far more widely with fans in order to gain majority approval for the re-design in the 2014-15 season after the opinion of only a small number was sought originally.
"It has been a full-on weekend for many Evertonians and undeniably you have spoken to us loudly and clearly. We have listened," said an Everton statement to supporters.
"We are sorry. It is clear that you wanted to be involved in the selection of our new club crest.
"We regret we didn't ask every Evertonian about something that matters so much to every one of you.
"We remain firm in the belief that our crest should be modernised - not a unique or unprecedented situation and one we know our fans would accept and embrace."