Brennan's remarks during an interview on MSNBC followed the White House's announcement that Trump would "deny Mr. Brennan access to classified information" by revoking his clearance.
In the interview, Brennan suggested Trump is lashing out because of his worries about the legal troubles increasingly looming over some of his associates.
"I think Mr. Trump is getting more and more concerned, more and more desperate and I would say more and more frightened, as there is closer and closer magnification of some of the things that those around him have been involved in," Brennan said. "So I do think it's important that I continue to speak out."
In a tweet shortly before his appearance on MSNBC, Brennan alleged that Trump's actions are "part of a broader effort" to "suppress freedom of speech & punish critics."
The White House first announced in July that it was considering stripping the security clearances of Brennan other former security and intelligence officials.
Brennan said on MSNBC that he did not hear about the revocation until he was told by a friend who had listened to the White House briefing on Wednesday, when the new policy was announced.
In a statement read by press secretary Sarah Huckabee Sanders, Trump accused Brennan of "lying" and conduct "characterized by increasingly frenzied commentary" that he said is "inconsistent with access to the Nation's most closely held secrets and facilitates the very aim of our adversaries."
Trump also said he was "evaluating action" with regard to the security clearances of ex-Director of National Intelligence James Clapper, former FBI Director James Comey, ex-Deputy Attorney General Sally Yates, former national security advisor Susan Rice and former Deputy FBI Director Andrew McCabe.
The Trump administration said it will also look at recently fired FBI employee Peter Strzok, a onetime leading member of special counsel Robert Mueller's probe of Russian meddling in the 2016 presidential election who was taken off that team following the discovery of anti-Trump text messages he sent.
The recipient of those texts, ex-FBI employee Lisa Page, was also included on the list.
All of those former government officials have critical of Trump; some of them have been vocal advocates against him. The White House has denied that the move constitutes an attempt by Trump to punish his critics.
But the last name on the list, who has been publicly silent about the president, is also a current employee of the FBI: Bruce Ohr.
Ohr is not a member of the special counsel's team, which has become a regular target of Trump's ire on Twitter. But Ohr's wife, Nellie, worked for intelligence gathering firm that produced a dossier alleging salacious connections between Trump and Russia.
The Mueller probe's detractors, including GOP members of Congress such as Rep. Jim Jordan of Ohio, have singled out Ohr's relationship to that firm, Fusion GPS, as evidence of corruption at the roots of the investigation.
Trump put Ohr in his sights in a tweet on Tuesday.
"Is this an effort to try to cow individuals inside and outside the government to make sure they don't say anything, either that is critical of Mr. Trump or with which he disagrees?" Brennan asked.
"I've seen this type of behavior and actions on the part of foreign tyrants and despots and autocrats in my national security career," he added. "I never thought I would see it here in the United States."
Brennan is a contributor to NBC News and MSNBC.