Brennan's stern words -- which sparked a quick Twitter retort from Trump -- were the latest salvo in the ongoing feud between the incoming Republican leader and US intelligence agencies, who have concluded Moscow meddled in the November election.
The 70-year-old Trump, who takes office on Friday, has nevertheless been effusive in his praise of Vladimir Putin, saying that if the Russian leader "likes" him, it would be an "asset" to help repair strained ties with Moscow.
The Senate Intelligence committee meanwhile has launched a bipartisan probe into Moscow's alleged interference in US politics -- which could force officials in both Barack Obama's administration and Trump's government to testify.
"I don't think he has a full appreciation of Russian capabilities, Russia's intentions and actions," Brennan said of Trump on Fox News Sunday.
"I think Mr. Trump has to be very disciplined in terms of what it is that he says publicly," Brennan said.
"He is going to be, in a few days' time, the most powerful person in the world, in terms of sitting on top of the United States government and I think he has to recognise that his words do have impact," the CIA chief added.
"He's going to have the opportunity to do something for national security as opposed to talking and tweeting," he said.
"Spontaneity is not something that protects national security interests."
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'Distraction'
US intelligence agencies allege that Putin ordered a covert effort to interfere in the election to boost Trump and harm his opponent, Democrat Hillary Clinton.
A report from the Director of National Intelligence released this month said hackers working for Russia penetrated Democratic Party computers and accounts to release files embarrassing to Clinton, and also conducted a campaign of media manipulation with the same aim.
Trump's feud with intelligence agencies has been stoked by the leak of an unsubstantiated report that Russia had gathered compromising personal and financial material on the president-elect, and alleged close links between Trump and Kremlin aides during the campaign.
Hours after Brennan's rebuke, Trump slapped back at intelligence leaders on Twitter, echoing the words of Pulitzer Prize-winning journalist Bob Woodward, who called the alleged Russia "kompromat" dossier "garbage."
"Thank you to Bob Woodward who said, 'That is a garbage document...it never should have been presented...Trump's right to be upset (angry)...about that...Those Intelligence chiefs made a mistake here, & when people make mistakes, they should APOLOGIZE.' Media should also apologize," Trump tweeted.
Incoming Vice President Mike Pence on Sunday dismissed notions that the Trump team and the Kremlin had made contact during the 2016 race.
"This is all a distraction," he said on NBC's Meet the Press. "It's all part of a narrative to delegitimise the election and to question the legitimacy of his presidency."
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'Salacious allegations'
The unsubstantiated dossier about Trump, Russia and possible compromising material -- compiled by a former British MI6 intelligence agent doing opposition research for Trump's campaign opponents -- also said Moscow had incriminating video of the president-elect.
The fact that intelligence agencies had offered Trump a synopsis of the dossier -- which was later published in full online by BuzzFeed -- lent the allegations credence.
But Brennan said the intelligence community was only "making sure that the president-elect was aware that it was circulating."
"I think there are some very salacious allegations in there -- again, unsubstantiated," he said, adding it was "a responsibility in the minds of the intelligence directors" to inform Trump as well as the Obama White House of the report.
Brennan bristled at Trump's likening of the US intelligence community to Nazi Germany, calling it "outrageous."
"I do take great umbrage at that," the outgoing spy chief said.
Pence blamed the scandal on "media bias," in an interview with CBS.
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