The updated design no longer features the club motto 'nil satis nisi optimum' - meaning 'Nothing but the best is good enough' - that has been present since 1991.
Goodison Park chiefs said the new version formed "a concise, modern and dynamic representation of Everton", and was produced after consulation with various stakeholders, including fans.
But there was widespread criticism on social media and an online petition garnered more than 6,000 signatures within hours of the crest being unveiled.
A statement on the Everton website, attempting to explain the re-design, said: "The previous version of the crest - created 13 years ago - was often misrepresented, suffering regularly from the omission of key elements like our name and our year of formation.
"As technology marches on, those challenges have increased. On television, on websites, on mobile devices, the crest was far too often badly reproduced.
"Our team carries a responsibility to maintain a refreshed and relevant identity for the club. We recognised the need to do this with diligence and sensitivity - with one eye on the past but also one eye on the future.
"We researched our history, we reviewed the evolution of our crest and we benchmarked against other major sporting brands.
"Created following an extensive consultation process with fans, supporters' groups and branding experts, our new club crest combines four historic elements of the outgoing crest - the tower, the shield, our name and the year of our formation - to form a concise, modern and dynamic representation of Everton."
The club added: "The name Everton and the 1878 date have been incorporated into the shield which does not feature the Latin motto.
"Although 'Nil Satis Nisi Optimum' is not included in this new design, it will still have a high-profile presence throughout the club, and a new range of retail products are being introduced."