"I suffer from panic attacks," an Italian passenger, Ivana Codoni, was quoted by the ANSA news agency as saying at the trial in Grosseto near the scene of the January 2012 disaster on Giglio Island in Tuscany.
"I never had any before the shipwreck. Now I am under constant medical monitoring," she told the court.
"The staff were telling us to go back to our cabins but we knew it was a trick," she said, adding: "We escaped to the external decks. We were operating on our own."
A Romanian survivor, Liliana Dobrian, said: "The waiters did not know what to say, what was happening."
"Since the shipwreck my husband and I have not been able to sleep. We get headaches. We had to go to a psychiatrist. We suffer from fear and anxiety," he said.
Luigi D'Eliso remembered that "people were going crazy".
"They punched at furniture in the restaurant. They were bleeding," he said, remembering that when staff were asked what to do, they answered: "We don't know".
His wife, Rosanna Abbinante, said: "They told us there was a technical fault but we realised that wasn't true".
Another, Claudia Poliani, said: "We were panicking, falling over. It was dark and nobody helped us.
Representatives of ship owners Costa Crociere, Europe's biggest cruise operator, also on Monday met with government officials in charge of the salvage operation.
ANSA said a new timetable for the removal of the ship presented by Costa Crociere said this could happen on July 18th-20th instead of June as previously planned.
The salvage is the biggest of a passenger ship ever attempted and last year saw the righting of the ship, which had been lying on its side since the accident.
The ship crashed into rocks off the Tuscan island of Giglio with 4,229 people on board and keeled over on the night of January 13th 2012 with the loss of 32 lives.
Its captain Francesco Schettino is on trial for manslaughter, causing a shipwreck and abandoning the vessel before all its passengers had been evacuated.