In an interview with CNN's Brian Stelter, Fallon referenced Spicer's comments during his first White House press briefing on Saturday, in which he berated the gathered media
for reporting that President Donald Trump's inauguration crowd had been smaller than that of President Barack Obama's.
"This was the largest audience to ever witness an inauguration, period," Spicer told journalists, a claim that is inaccurate
. He went on to accuse the media of posting photos that were "intentionally framed" to make Trump's crowd look smaller, an assertion that left many members of the press stunned.
Spicer's comments, Fallon told Stelter, were "an affront to anybody who is on our side of the wall and works in this business."
"I'm concerned, if yesterday's briefing is any indication, that this is somebody who will put his standing with his boss ahead of his integrity and standing with the press corps. Those are things that are dangerous territory," he said.
"You cannot tell a lie," he continued, adding, "he told a fundamental untruth."
Spicer needed to start standing up to his boss, Fallon said, referring to Trump's appearance at the CIA two hours before Spicer's press briefing, in which Trump also blasted the press and referenced his "running war" with the media
"Sean Spicer went out and double downed on it," Fallon said.
As a press secretary, Spicer has a moral duty to be governed by objective truth rather than the whims of his superiors, Fallon said.
"This is somebody who's going to put his standing with his boss ahead of his integrity and his standing with the press corps," Fallon said.
"It was clear intent. If he was put in the situation by Reince Priebus or his boss, Donald Trump, to go out to tell a lie to the American people, he should have resigned rather than go out and take the podium."
Asked by Stelter if he personally would have resigned if put in the same position, Fallon said he would.
"I would like to think I would have too much integrity to go out and look in the cameras and say something that was provably false," he said.
Fallon said the American people should be troubled.
"If they're willing to lie about something as trivial as crowd size at the inaugural, think of what they might be willing to lie about, matters of war and peace and other things that are far more serious," he said.
"We need to call them out," he added.
Spicer has not commented on the briefing, but Trump senior adviser Kellyanne Conway on Sunday defended Spicer on NBC's "Meet the Press,"
saying Spicer's claims were "alternative facts."
"You're saying it's a falsehood. And they're giving -- Sean Spicer, our press secretary -- gave alternative facts," she told host Chuck Todd.