Smith posted a picture of a semi-nude woman on his account late Thursday night.
He told reporters in Milwaukee on Friday night that he regretted the tweet.
"I didn't know it was going to be as big a deal as it is now," Smith told reporters on Friday. "I definitely regret it. Anytime I do anything that takes away from our team, I'm definitely going to regret it."
Smith said on Sunday that he has no plans to appeal the fine.
"I can't worry about off-the-court stuff, our issue right now is on the basketball court," Smith said after the Knicks lost to the Philadelphia 76ers, 106-94, on Sunday for their fifth straight defeat.
Smith appears to have eventually deleted the post but that didn't stop the photo from being passed around the Internet on Friday, earning significant attention that included a mention on the sports website Deadspin.
Smith later posted a message directed to the woman, saying, "Things are being taken (too) far sorry @therealtahiry."
The Knicks declined to comment on Smith's tweet and the NBA's decision to fine him for it.
Smith signed with the Knicks on Feb. 17 after playing a stint in China that started during the NBA lockout.
The 26-year-old New Jersey native has been inconsistent thus far in New York, averaging 8.9 points in 22.4 minutes in his first nine games.
Ian Begley is a regular contributor to ESPNNewYork.com. Information from The Associated Press was used in this report.