Following revelations of the scandal, the hashtag #DeleteFacebook circulated online. Even Brian Acton, the co-founder of WhatsApp, a company that Facebook bought for $19 billion in 2014, tweeted the hashtag.
Analysts have been concerned about the knock-on effect the fiasco would have on user numbers, but Zuckerberg said he had not seen lots of people leaving the social network.
"I don't think we've seen a meaningful number of people act on that, but, you know, it's not good," Zuckerberg told The New York Times on Wednesday about the hashtag.
"I think it's a clear signal that this is a major trust issue for people, and I understand that. And whether people delete their app over it or just don't feel good about using Facebook, that's a big issue that I think we have a responsibility to rectify."