Passengers onboard a Southwest Airlines flight from Tampa to Raleigh, N.C., Tuesday thought their lives were over when they say the pilot announced an emergency and the plane suddenly dropped thousands of feet.

"We were clenching hands and we were saying, 'I love you," passenger Phyllis Fann told ABC News' affiliate WTVD. "I just shut my eyes waiting for it to be all over."

The FAA is now investigating the pilot's decision to put the Boeing 737 into a nosedive. Southwest Airlines says the issue was a problem with cabin pressure and that the pilot radioed in an emergency when a cockpit alarm showed a problem with the plane's pressurization. Standard procedure is to lose altitude as quickly as possible.

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"As part of the procedure to resolve the issue, the captain notified the cabin using the public address system that he was going down to a lower altitude just before an unplanned but controlled descent. The maintenance issue was resolved before the flight safely landed at Raleigh-Durham," Southwest said in a statement.

The plane dropped about 20,000 feet in 11 minutes. That descent is not out of the ordinary, but the emergency warning from the pilot over the plane's public announcement system made passengers think the end was near.

"He said, 'We're going down,'" passenger Shelley Wills told WTVD. "And everyone is looking around like, 'Is this a joke? Is he serious? And then you felt the nosedive."

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Wills recounted images of passengers, including herself, grabbing their cellphones to text their loved ones one last message.

"It says, 'I love you Alyssa. My plane is going down,'" she said of her own text message to her daughter.

Passengers told WTVD they received an email from Southwest Airlines after the flight explaining that the pilot's warning was meant for crew members only.

"When the pilot came on the PA system he specifically addressed the passengers and the crew at the same time," passenger Kevin Emery told WTVD, recalling the incident differently. "You could tell he was struggling, maybe putting on an oxygen mask, something kept hitting the mic. Then the last thing he said was, 'We're going down.' I understand it was the heat of the moment, it's just one of those things you never want to hear on an airplane."

The Southwest Airlines flight and its 96 passengers and five crew members all landed safely at Raleigh-Durham International Airport after the scare.

Southwest issued $200 travel vouchers to the passengers.

Passengers like Emery and Fann say they are disappointed in how Southwest handled their situation.

"That's just an insult to the passenger's intelligence," Emery said of offering the $200 voucher without an apology or explanation.

"It was not treated like it was a special flight in that we had a horrifying experience," Fann said. "We just landed and then we departed the plane."