It comes after general manager Danny Ferry took a leave of absence following his racially insensitive remarks about NBA forward Luol Deng.
In an open letter, Koonin wrote the Hawks had let down players, employees, fans and the city by failing to act sooner.
Koonin said the "shortcomings are beyond a single email, a single person or a single event".
"To the contrary, over a period of years, we have found that there have been inflammatory words, phrases, inferences, and innuendos about race," he wrote.
"We as an organisation did not correct these failures. We did not do the right thing."
Koonin described himself as "angry" and "deeply saddened", but he wants to oversee change at the Hawks.
Part of the plans include working with a diversity consultant and hiring a chief diversity officer.
"We should embody civility, sportsmanship, and human decency and we will demand that we exceed these standards," Koonin wrote.
"We ask our staff and players to continue to do great work and to play hard.
"We ask our fans to continue to support our players as we all learn through this process " we should not punish them.
"We aim to win as a collective team both on and off the court."