The Israeli parted company with the West Africans following the expiration of his contract last month.
The 62-year-old's last assignment was at the 2017 Africa Cup of Nations in Gabon, where the Stars reached the semi-finals.
“He [Grant] knows he failed," Osei told Kasapa FM.
"Let’s ask ourselves the legacy he left as head coach of the Black Stars.
“He failed to meet his target and his approach to the work was uninspiring.
"Why are Ghanaians calling for a competent coach [this time around]? Because they don’t want the mistake of appointing someone who will not dedicate himself to the work.
“He actually left no legacy as head coach of the Black Stars. What will he be remembered for now that he is gone? Nothing!"
Ghana are on the brink of missing out on the 2018 Fifa World Cup in Russia, following a poor start to the final round qualifiers.
The Black Stars have just one point to their name in Group E, five clear points adrift of leaders Egypt.
Grant led Ghana to the final of the 2015 Afcon, losing to Cote d'Ivoire on penalties - only two months into his tenure.
Osei doubles as the vice-chairman of the Black Stars Management Committee.