The Black Stars have been treated with apathy since their poor campaign at the 2014 Fifa World Cup in Brazil - a competition they exited at the group stage.
Ghana are set for yet another tournament, where they will play in Group D alongside Egypt, Mali and Uganda.
“We know they have been supporting us," Acheampong told TV3.
"The only thing they want from us is to make them happy.
“Maybe on one or two occasions, we couldn’t achieve what they wanted.
"They can be angry, but I'm just pleading with them to put all this aside.
"This is a New Year, a new tournament, they just have to support us with everything. That is the only way we can progress.”
Ghana play Uganda in their Afcon opener on Tuesday, before facing Mali and Egypt on January 21 and 25 respectively.
The Black Stars, who are four-time winners of the championship, placed second at the 2015 edition following a penalty defeat to Cote d'Ivoire.
Acheampong was part of Ghana's set-up at Equatorial Guinea 2015, missing his kick in the final shootout.