The American billionaire - who is best known as the founder of the company - made the claim during a Q&A session with US senators in the wake of the recent Cambridge Analytica data collection scandal.
During the much-discussed meeting, Zuckerberg revealed: "This is an arms race. They're going to keep getting better."
He admitted, too, that Robert Mueller - who is the special counsel investigating alleged Russian involvement in the US election in 2016 - has interviewed some of his staff at Facebook about the issue.
However, Zuckerberg - who was not among those interviewed - added: "Our work with the special counsel is confidential and I want to make sure that in an open session I'm not revealing something that's confidential."
Zuckerberg, 33, also insisted that Facebook is doing everything it can to combat the Russian threat.
He shared: "There are people in Russia whose job it is to try to exploit our systems and other internet systems and other systems as well. We need to invest in getting better at this too."
During the course of the sessions, Zuckerberg was asked whether Facebook should face tighter regulations in light of the recent revelations.
The businessman replied by explaining that while he would would welcome regulation, it needed to be the "right regulation".
Meanwhile, Senator John Kennedy warned him: "I don't want to have to vote to regulate Facebook. But by God, I will. That depends on you ... Your user agreement sucks."