NEW YORK (CNN) -- After a YouTube video showed panicked New Yorkers scrambling as a Boeing 747 flew frighteningly close to the lower Manhattan skyline, a former Homeland Security adviser questioned whether the man who approved the flyby should remain in his White House office.
Witnesses reported seeing a plane circle over the Upper New York Bay near the Statue of Liberty.
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Fran Townsend, who advised President George W. Bush for more than three years, called the move "crass insensitivity" in the wake of 9/11.
"I'd call this felony stupidity. This is probably not the right job for Mr. Caldera to be in if he didn't understand the likely reaction of New Yorkers, of the mayor," Townsend said Tuesday on CNN's "American Morning."
Louis Caldera, director of the White House Military Office, quickly apologized for Monday's incident after the planes prompted workers and residents to evacuate buildings in New York and New Jersey.
Watch Townsend slam Caldera »
"Last week, I approved a mission over New York. I take responsibility for that decision," Caldera said. "While federal authorities took the proper steps to notify state and local authorities in New York and New Jersey, it's clear that the mission created confusion and disruption."
The Federal Aviation Administration said the aircraft, which functions as Air Force One when the president is aboard, was taking part in a classified, government-sanctioned photo shoot.
An angry Mayor Michael Bloomberg said it "defies the imagination" that an agency would schedule the photo shoot so near the site of the
September 11, 2001, attacks on the World Trade Center.
President Obama also reportedly expressed outrage. Sen. Charles Schumer, D-New York, said the FAA's decision to not announce the flyby "borders on being either cruel or very, very stupid."
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Witnesses reported seeing the plane circle over the Upper New York Bay near the Statue of Liberty before flying up the Hudson River.
Watch the plane fly over Manhattan »
The YouTube video shows dozens of people standing in a parking lot, watching the plane approach. As it nears, they begin to run. Someone unleashes an expletive. "Run, run!" says one person. "Oh my God," cries another.
Two officials said the White House Military Office was trying to update its file photos of Air Force One. The officials said the president was angry when he learned Monday afternoon about the flight.
"The president was furious about it," one of the officials said.
On Tuesday, Obama told reporters, "It was a mistake. It was something we found out about along with all of you. And it will not happen again."
Bloomberg said he, too, was perturbed.
Watch the White House apologize »
"I'm annoyed -- furious is a better word -- that I wasn't told," he said, calling the FAA's decision to withhold details about the flight "ridiculous" and "poor judgment."
"Why the Defense Department wanted to do a photo op right around the site of the World Trade Center defies the imagination," he said. "Had we known, I would have asked them not to."
Linda Garcia-Rose, a social worker who counsels post-traumatic stress disorder patients in an office three blocks from where the World Trade Center stood, called the flight an "absolute travesty."
Watch the White House respond to questions about the scare »
"There was no warning. It looked like the plane was about to come into us," she said. "I'm a therapist, and I actually had a panic attack."
Garcia-Rose, who works with nearly two dozen patients ages 15 to 47, said she was inundated with phone calls from patients.
"They're traumatized. They're asking 'How could this happen?' They're nervous. Their anxiety levels are high," she said.
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Garcia-Rose said she is considering filing a class-action suit against the government for sanctioning the plane's unannounced flight.
"I believe the government has done something really wrong," she said.
Capt. Anna Carpenter of Andrews Air Force Base in Maryland said local law enforcement agencies and the FAA had been given notice of the exercise.
New York Police Deputy Commissioner Paul J. Browne said the department had been alerted about the flight "with directives to local authorities not to disclose information about it."
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