Chesley Sullenberger, the US Airways pilot who landed his plane in New York's Hudson River with all onboard escaping safely, waves during a homecoming celebration on Jan. 24 in Danville, Calif. ((Noah Berger/Associated Press))

The pilot and crew of the plane that landed last month in New York's Hudson River with all onboard escaping death spoke about their ordeal for the first time as a group in an interview with CBS's 60 Minutes on Sunday.

"It was the worst sickening, pit-of-your-stomach, falling-through-the-floor feeling I've ever felt in my life," said Capt. Chesley Sullenberger as he described to interviewer Katie Couric the tense, final moments of US Airways Flight 1549 on Jan. 15 after it took off from LaGuardia Airport and was struck in both engines by birds. "I knew immediately it was very bad."

"Did you think, 'How are we going to get ourselves out of this?' " Couric asked.

"No. My initial reaction was one of disbelief," said Sullenberger, a former U.S. air force fighter pilot with 42 years of flying experience who instructs flight crews on how to respond to crises in the air. " 'I can't believe this is happening. This doesn't happen to me.' "

Sullenberger took control of the aircraft from co-pilot Jeff Skiles and began making the decisions and manoeuvres that resulted in an emergency landing.

About 30 seconds after the birds struck, Sullenberger radioed air-traffic control at LaGuardia, informing it of the situation and that he needed to return to the airport to land. But he quickly determined that it would be problematic to reach the runway there and considered Teterboro Airport in New Jersey. It became clear to him he couldn't make it there, either.

He then spoke again to the controller, saying, "We're going in the Hudson."

Co-pilot Skiles relayed his perspective to CBS of his duties in the cockpit. Flight attendants Donna Dent, Sheila Dail and Doreen Welsh provided a gripping account of what they heard, saw and felt in the aircraft's cabin. The 150 passengers were told to "brace for impact" as the jetliner angled down toward the river, relying on Sullenberger's skills to prevent a catastrophe.

Within seconds of the landing, the crew was helping passengers out of the aircraft, and minutes later first responders from New York City arrived to rescue passengers as the plane sank into the freezing water.