The 62-year-old actor confirmed he quit Twitter in an Instagram video Wednesday.
Baldwin deactivated his account after referencing Anderson "switching accents" in a tweet Wednesday. Fans were surprised to hear Anderson, who grew up in London and has played many British roles, speak in an American accent at the Golden Globes on Sunday.
Baldwin re-posted a CNN story titled, "Gillian Anderson's American accent throws some people off" and tweeted, "Switching accents? That sounds...fascinating."
Baldwin's wife, Hilaria Baldwin, had faced backlash in December after her Spanish accent and heritage were called into question. Hilaria Baldwin later said she was born in Boston but grew up spending time in Spain. She also clarified that her given name is Hillary.
In his video Wednesday, Baldwin appeared to address his remarks but did not mention Anderson by name.
"Wanted to post a quick video to say that I deactivated my Twitter account today," he said. "I just wrote, 'Oh, that's interesting.' And of course, you can't do any irony on Twitter -- you can't do any irony in the United States anymore because the United States is such [an] uptight, stressed-out place and such an unpleasant place right now."
Baldwin said he is a "huge fan" of Anderson's and didn't mean to offend her. He said he was trying to illustrate the point that if people are influenced by multiple culture, "that's your business."
Baldwin said he "can't say anything dark enough" to describe Twitter users.
"The problem with Twitter is, there was a lot of haters," he said.
Baldwin had slammed "ridiculous" and "false" reports in December amid the controversy over Hilaria Baldwin's heritage.
"We live in a world where we're hidden behind the anonymity of social media, and people feel like they can say anything," he said. "They want to spray it all over you and spit it all over you, their venom and their hate."
Baldwin and Hilaria Baldwin have five other children, daughter Carmen, 7, and sons Rafael, 6, Leonardo, 4, Romeo, 2, and Edu, 5 months. Alec Baldwin also has a daughter, Ireland, 25, with his ex-wife, actress Kim Basinger.