The chief executive also stressed that Facebook is in an "arms race" with Russian Federation and that the company will work on finding fake accounts that are trying to expose data.
But Florida Senator Bill Nelson declared: "If you and other social media companies don't get your act together, none of us are going to have any privacy any more".
He was also asked about the alleged abuse of the social media platform by Russian groups to interfere in the 2016 USA presidential elections.
Mark Zuckerberg tells senators: Sorry, mistakes are mine
"We face a number of important issues around privacy, safety, and democracy, and you will rightfully have some hard questions for me to answer", Zuckerberg said.
Three Russian companies and 13 Russian individuals have been charged, while past year Facebook banned 944 suspicious accounts associated with Russia's Internet Research Agency.
Mr Zuckerberg said the company was now developing new tools to identify fake accounts.More news: DOJ Relents, Provides House Intel With Crucial Russia Probe Document
MZ:"There are people in Russian Federation whose job it is to try to exploit our systems and other internet systems".
Another lawyer in the case, Jason McCue, said "the defendants effectively abused the human right to privacy of ordinary Facebook users".
"We believe it is entirely possible that there will be a connection there", Zuckerberg said when asked if there was overlap between Cambridge Analytica's harvested user data and the political propaganda pushed by the Kremlin-linked Internet Research Agency during the 2016 presidential election.More news: High-speed chase involving stolen auto ends in Clark County
The news that a personality quiz developed by an academic, Aleksandr Kogan, had collected data not just from the people who used it but also from their Facebook friends was revealed by newspaper investigations. "This includes the basic responsibility of protecting people's information, which we failed to do with Cambridge Analytica".
These notifications are part of Facebook's attempts to deal with the global scandal where information about its users was accessed improperly by third-party companies.More news: Instagram 'Focus' brings support for Portrait shots: Here's how it will work
Zuckerberg also agreed to greater regulation of his company, according to the Times, and to help Congress frame regulations for tech companies including supporting a rule to notify users of a data breach within 72 hours.