Paa Kwesi Fabin's side topped Group A despite a 1-0 defeat to the United States and will lock horns with Niger in the Round of 16 on Wednesday.
"I doubt Ghana team can win the trophy. This is because if you look at the performance of the other countries left in the tournament and the number of goals they are scoring, you'll be scared," Obodai told Happy FM.
"Look at the United States' game against Paraguay yesterday. They dispatched the Paraguayans by five goals which nobody saw coming.
"Ghana are not scoring enough but one will argue that we defeated India 4-0 to top Group A. The Indians were afraid of us even before the start of the match. They were expecting us to humiliate them at least by six goals but they only conceded four and were happy with it.
He added: "However, tomorrow's game will tell us where we'll reach in this competition. Having said that, I don't expect them to exit the tournament in the next game or two but I'm tipping them to end their adventure somewhere at the semifinal stage. For winning the trophy, I doubt it."
Obodai was part of the Ghana squad that participated in the 1999 edition of the competition held in New Zealand.