The Black Stars failed to end their sprawling 35-year drought in Gabon, falling at the hands of eventual winners Cameroon in the semi-finals.
There was even more disappointment for the team on Saturday following a 1-0 loss to Burkina Faso in the third-place playoff.
"It was the dream and wish of all Ghanaians to win the prestigious cup [at] Afcon 2017 but unfortunately we couldn't attain that goal," Partey wrote on Facebook.
"We are sorry for disappointing all Ghanaians around the world who have given us the massive support and rallied behind us since day [one].
"Nevertheless, all I can say is a big thank you to Ghana for giving me this opportunity to serve my beloved country.
"All is not lost and we hope to come back strongly next time and bring joy to the faces of all Ghanaians."
Partey played all but one of Ghana's games at the Afcon.
The only exception was the third group game, by which time the Black Stars had already secured qualification to the quarter-finals.
The Atletico Madrid man was among seven Afcon debutants in Ghana's set-up.
The four-time champions, who have made the semi-finals of the last six tournaments, must now wait until 2019 to make yet another attempt to claim gold since 1982.