The penalty shootout loss (5-4) to Tunisia following a 1-1 stalemate after extra-time saw the West Africans dumped out of the continental championship in the Round of 16, the first time they have failed to make the quarter-finals of Afcon since 2006.
The setback also prolongs Ghana's wait for a first Afcon title since 1982.
“I am very sad and disappointed we could not get to the next stage but we need to take heart and be stronger," Ayew told the media in Egypt.
"The entire team gave everything but it did not go our way.
“As a Ghanaian and as a leader, no player is to be held responsible for this: I take all the responsibilities and we are going to work hard and come back stronger.
“If we have been kicked out at this stage it means we had a bad tournament and since we couldn’t achieve the mission we came here for, I will say we failed."
In normal time, Taha Yassine Khenissi broke the deadlock for Tunisia in the 73rd minute before Rami Bedoui's own goal in injury time leveled the score for Ghana.
Caleb Ekuban's missed penalty ultimately proved the deciding factor at Ismailia Stadium.
Ghana have now lost their last four shootouts at Afcon after winning their first one against Libya in the 1982 final.