"The new administration -- and any president -- needs to recognize that this is a challenging and dangerous world, and that the intelligence community and intelligence professionals can help to keep this country safe and protect our national security interests," Brennan said during a joint podcast with the University of Chicago's Institute of Politics and CNN.
"Any president or administration that does not recognize that is one that is putting this country's national security at great risk and peril," he added.
Trump has repeatedly taken stances at odds with the intelligence community's findings that Russia was behind a campaign aimed at influencing last year's presidential race.
After meeting with intelligence chiefs, including Brennan, last Friday, Trump acknowledged in a statement after the meeting that Russia and others sought to hack the Democratic National Committee (DNC), but maintained the efforts had "absolutely no effect" on the end results
The hacking of the DNC as well as Clinton campaign chairman John Podesta revealed unsavory details about how the organization allegedly conspired to favor Clinton against Bernie Sanders to win the Democratic Party's nomination.
Trump's briefing was quickly followed by the public disclosure of an unclassified report chronicling Moscow's alleged campaign.
In it, America's intelligence agencies assessed that Russian President Vladimir Puttin directly orchestrated a sweeping campaign aimed at undermining Democratic nominee Hillary Clinton in favor of Trump.
In addition, the Kremlin used its state-owned media apparatus, RT, and paid trolls "as part of its influence efforts to denigrate" Clinton.
Brennan maintained intelligence agencies "have great confidence" in their assessment.