The AC Milan man is reported to have refused to warm-up ahead of the game, which ended 2-1, and the case is now being reviewed by the nation's FA after coach Kwesi Appiah cited the episode in his technical report.
The ex-Chelsea midfielder has urged “decent dialogue” to resolve issues over appearance fees and training ground indiscipline instead of “destructive and vicious attacks and counter attacks on individual members of the team".
He said in a media statement: “I hold the view that we can investigate and resolve these issues without further destroying the team.
“I therefore 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 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 Ghanaian football. I strongly believe that it is absolutely the right thing to do for the good and prosperity of our nation's football.”
Essien added: “It is in keeping with the positions stated above that I have decided to refrain from responding to the GFA’s allegation that I had displayed acts of indiscipline before and during the Portugal game in Brazil.
"In deciding not to respond to the allegations, I am convinced that in the fullness of time, all the facts surrounding the entire episode will become public for the good people of Ghana to judge my guilt or otherwise.”
Kevin-Prince Boateng was sent home from the competition for an alleged verbal attack on Keshi, while Sulley Muntari was also ordered to leave the camp over a reported unprovoked assault on a Ghana official.
The African nation finished fourth in Group G with just a point and failed to make it to the knockout stage of the competition for the first time in the last three World Cups.