Kosmina announced on Monday he was stepping down from the role, citing a "lack of trust" in the way the A-League club was being run.
Adelaide sits fourth on the A-League ladder with 10 wins from 18 matches and six losses, with two draws.
Kosmina's resignation comes despite the club enjoying a strong season in his second stint as coach.
United is six points behind competition leaders Central Coast.
The 56-year-old told footballaustralia.com.au that he was making the decision with no regrets.
He felt Adelaide could still have a successful season but hit out strongly at the way the club was being run.
"Before last weekend, we had been first or second in the league and were recognised as a good football team," Kosmina said in a statement.
"However, apart from survival, I can see no clear direction.
"There is no vision. Decision-making at management level is reactive and impulsive at best and there is no consistency in managerial procedure.
"There is far too much whispering in corridors and around corners. I feel sorry for (owner) Rob Gerard, and I also feel for directors Richard Noble and Phil Lounder - people I trust.
"But I simply cannot and will not, work in an environment which otherwise lacks trust."