Kwesi Appiah's men were eliminated from the competition in Brazil at the group stage having picked up just one point from their clashes with the United States, Germany and Portugal.
Off-field issues also caused disruptions in the Ghana camp with disagreements over appearance fees followed by the indefinite suspensions of Kevin-Prince Boateng and Sulley Muntari.
Boateng subsequently described Ghana's setup as "amateurish", while the country's football association confirmed they were to investigate Essien for allegedly failing to warm up prior to their Group G finale against Portugal.
On Wednesday, Appiah spoke of a determination to avoid disciplinary problems in future amid Essien refusing to confirm or deny the allegations.
Essien did, though, speak of a need for all involved to remain level-headed in their assessment of the Black Stars' World Cup campaign and subsequent fall-out.
"Like any other patriotic Ghanaian, and as an avid supporter and member of the Ghana Black Stars, I am deeply embarrassed and devastated by the team’s failure to make, at least, [the] semi-final berth we had publicly promised the good people of Ghana ahead of our departure from Accra," he told Citi FM.
"While I will be the first to concede that not everything went according to plan before and during our participation in the tournament, I believe that destructive and vicious attacks and counter attacks on individual members of the team as well as the technical and management team are not the solution to the Ghana Black Stars' problems. Instead, we must all embrace peace and seek a lasting solution for the team's problems through decent dialogue.
"I... urge all of us who continue to make public comments on the team's painful experience of leaving the tournament as early as we did with just a point to be circumspect in our discourse.
"I also urge all involved to please remain calm and allow state authorities interested in investigating the issues at stake to do their jobs without any interference and come out with the truth.
"It is only then that we can learn from our mistakes and reform all aspects of our preparations for major football tournaments in order to restore the pride and glory of Ghana Football."
