Kudus Mohammed scored for the Black Starlets but it yielded little as Hadji Drame and Djemoussa Traore netted to ensure a 2-1 triumph for the Eagles.
It was Ghana's third consecutive defeat to the Malians in 2017.
“It is not our will to lose to Mali for a third time but it has happened," Ayiah said.
"I cannot really tell what caused the defeat but I can say that is how football is.
“It’s very painful that we are out from the tournament because we came here to write a new history."
In May, Ghana succumbed 1-0 to Mali in the final of the Africa U-17 Cup of Nations before falling once again last month, this time a 2-1 defeat in a friendly fixture ahead of the World Cup.
"The Malians are too much, they are a very strong team and they can win the title," Ayiah continued.
“We did our best and tried to win so we could qualify to the next stage but it didn’t happen.
“We must all rally behind them in prayer since we are all Africans - I know they can do it.”
Ghana made a return to the world youth championship for the first time since 2007.
Mali, meanwhile, face European champions Spain in the semifinals on Wednesday.