Last month, Wei called for the under-21 squad to become a wild card 17th team in the top flight Chinese Super League (CSL) with the under-19s and under-17s joining the second and third divisions.
The plan attracted widespread criticism from media and fans with some journalists suggesting Wei must have been "kicked in the head by a donkey", or lost his senses.
"It was a mistake to think that the traditional sports administrative style would adapt to professional sport," Wei told Monday's Beijing News.
"At least it was inappropriate. My intention was good but the proposal was imperfect and must be revised."
Wei, who built his name with success in heading China's water sports under the traditional state system, took over Chinese soccer in January after former CFA chief Nan Yong was arrested for corruption.
While his admission is unusual for a Chinese official, Wei remains adamant that more playing time would help the development of the national team, which is 84th in the FIFA rankings.
"What I am not admitting is that getting the national teams more time to train and matches to play is wrong," Wei added.
"Since it was a mistake, I won't insist the nationals teams play in the CSL. But we could invite the CSL clubs to play against the Olympic team, couldn't we?"
