Mr Lee called web users' efforts to exert a malicious influence on the chatbot "a coordinated attack by a subset of people".
"Although we had prepared for many types of abuses of the system, we had made a critical oversight for this specific attack," Mr Lee wrote.
"As a result, Tay tweeted wildly inappropriate and reprehensible words and images."
Microsoft has enjoyed better success with a chatbot called XiaoIce that the company launched in China in 2014.
XiaoIce is used by about 40 million people and is known for "delighting with its stories and conversations," according to Microsoft.
As for Tay? Not so much.
"We will remain steadfast in our efforts to learn from this and other experiences as we work toward contributing to an Internet that represents the best, not the worst, of humanity," Mr Lee wrote.
Microsoft deleted all offensive tweets sent by the bot on Thursday.