New York (CNN) -- Cellphone video captured by two New York-bound Delta Air Lines passengers Saturday night portrays the fear of an impending crash and the relief that followed when the pilot averted a catastrophic landing.

"Brace for impact," a deep voice says on the intercom.

"Heads down! Stay down! Heads down! Stay down!" a woman commands for more than 30 seconds.

Two passengers aboard Flight 4951 from Atlanta, Georgia, to White Plains, New York, taped the dramatic moments of their flight's emergency landing at John F. Kennedy International Airport in New York.

The passengers who shot the footage, Chase Benzenberg and Alessandro Albero, said Monday on CNN's "American Morning" that what first seemed amusing soon turned into a serious situation.

"While we were circling Westchester Airport, we circled for a good 20 minutes and we were joking around with each other, saying, 'I don't know if he knows where the landing strip is,' and then they made the announcement on the loudspeaker,"

Albero said.

"Alessandro was concerned that he was right next to the wing and he got to see the whole thing. So we didn't know if there was going to be sparks flying through the window, an engine flying through," said Benzenberg.

The footage from Flight 4951 shows sparks outside a window of the plane's cabin.

The flight experienced landing gear problems, according to a recording of a pilot's conversation with air traffic control.

"We have 64 souls on board," the pilot said, according to LiveATC.net, which provides audio from air traffic control radio communications.

"We've been running all the checklists and talking to our maintenance and approach, our maintenance and dispatcher and we have not been able to get the landing gear down," the pilot said. "Our preference would be to proceed over to JFK and execute an emergency landing over there ... and if it's not completely obvious, we just want to confirm, we are declaring an emergency."

After the pilot told passengers about the issues with the landing gear, "We're envisioning belly slide the whole way, with sparks," Benzenberg said. "But they actually came out later and said that there were -- it's only the right rear landing gear that would not come down, so it would be hitting the wing, which is actually what happened."

Benzenberg said the announcement upset some of the passengers.

"I saw the lady sitting in front of me who just had tears coming down and she was holding her husband's hand," he said. "Another lady was reaching for a life jacket, saying, 'I can't get it. It's stuck.' I said 'We don't need that right now. We're not going into water. Just listen to the instructions and try to stay calm.'"

The pilot and an air traffic controller arranged for the plane to land at JFK.

"Emergency equipment standing by midfield as a precautionary measure," the air traffic controller said.

The plane landed safely with no injuries reported.

"Landing was actually quite smooth. The pilot did a wonderful job," Albero said. "We came down and the plane tipped slightly and the sparks came up ... It was pretty intense, but they did a wonderful job."

Albero said the landing was "an incredible moment," with everybody clapping, then hugging and shaking hands after an immediate evacuation.

In retrospect, the men say the situation was not as dire as their video made it seem.

"[The flight attendant heard on the tape] actually made it more intense than I think it really was. But that's what's the right thing to do in that situation," said Benzenberg.

He added, "Initially, we would say that we survived a plane crash, but it's kind of -- after it was all finished, I almost hoped it was a little bit more bumpier or something just so we had a cooler story, but we're just happy to be safe."

Albero's girlfriend may have been among those most concerned. Albero drained his phone's battery taping the incident, so after telling his girlfriend the plane was making an emergency landing, he was unable to call her back. He eventually contacted her on Benzenberg's cellphone.

The Federal Aviation Administration has not released a cause for why the plane's landing gear malfunctioned.

CNN's Rick Martin, Ric Ward and Miguel Susana and contributed to this report.