The admission came hours after rescue teams brought two passengers and an injured crew member off the Costa Concordia to safety, but recovered the bodies of two men who had failed to make it off the vessel.
"It seems that the commander made errors of judgement that had serious consequences," said a company statement, adding that his management of the emergency had not followed company procedures.
Prosecutors arrested Captain Francesco Schettino and first officer Ciro Ambrosio late Saturday.
On Sunday Francesco Verusio, the prosecutor leading the investigation, told reporters Schettino had left the stricken liner "well before" the last passengers were evacuated.
And coast guard officials said the captain ignored repeated requests from them to return to his ship as the rescue operation continued.
Firefighters said that while the captain was already ashore just after midnight the last passengers were evacuated at around 0500 GMT.
Prosecutors have also said the crew mishandled the emergency, delaying the start of the evacuation until an hour after the accident.
Costa Crociere said it was cooperating with the prosecutors.
Earlier Sunday emergency teams rescued two South Korean honeymooners and an Italian crewman from the vessel, as it lay half-submerged off the west coast of Italy.
Fire brigade spokesman Luca Cari said the rescued South Korean honeymooners had been evacuated by helicopter and were in "perfect condition".
"They were in their cabin, we still don't understand why," he added.
The rescued Italian, an officer responsible for passenger security on the vessel, was found after emergency crews spent hours searching for him after hearing his voice echoing in the massive ship.
"He shouted with joy when we got to him. He just thanked us," fire crew chief Cosimo Pulito said, adding that the man had suffered a broken leg.
But divers also found the bodies of two men trapped in a cabin in the rear of the submerged part of the 17-deck liner, said the coastguard.
"I'm afraid that we could find others," Angelo Scarpa, one of the divers who recovered the bodies, told AFP.
One victim was identified as Spanish and another was Italian, said news agency ANSA, citing informed sources.
Rescuers said the search in the half-submerged ship was highly dangerous because the decks were at almost a 90-degree angle and there was a risk the ship could slip off the rocks it had struck and sink altogether.
But Pulito said they would keep searching until the whole ship had been covered.
The discovery of the bodies brought the death toll from the disaster to five, after the deaths were confirmed on Saturday of two French passengers and a Peruvian crew member.
Medical sources said around 60 people had been injured, two of them seriously: a woman with a blow to the head and a man hit in the spine.
Enrico Rossi, governor of the Tuscany region, said six crew members and 11 passengers were still unaccounted for.
The Costa Concordia, the luxury flagship of the Costa Crociere's fleet, was carrying more than 4,200 people when it hit the rocks before running aground just off the Tuscan island of Giglio on the evening of Friday the 13th.
Several passengers have described the confusion on board as the lights went out and how they were at first told it was just an electrical fault -- before the ship lurched sharply on its side and the panic started.
"In one corridor we smashed a window and took the life jackets," one passenger, Antonietta Simboli, told Italian newspapers.
"But as there weren't a lot of them, we were stealing them from each other," she added.
US national Amanda Warrick described to CNN television how the situation degenerated.
"Those were the most chaotic moments because everyone was pushing, shoving each other, trying to get on a life boat. It was chaos."
French tourist Olivier Carrasco said he would sue the cruise operator.
Concordia: 'temple of fun' becomes a scene of tragedy
"We saved ourselves in complete disarray. It took an hour and a half before a real alert was sent out," he told French news website South-West, adding that the light on his lifevest failed.
Rescuers said they plucked 100 people from the sea overnight Friday/Saturday.
Island residents have already said the ship was sailing far too close to Giglio and had hit an underwater rocky reef well known to inhabitants.
Defence Minister Giampaola Di Paola described it as "a serious human error that has had dramatic consequences."
Investigators on Sunday started analysing a "black box" recovered by rescuers, which logged the 291-metre long ship's movements and conversations between personnel.
But Italian media are already reporting that the two officers could face charges of multiple homicide and abandoning the ship before all the passengers were rescued.
Other crew members however said that they participated in evacuations.
Colombian crewman Edgard Lopez Sanchez told AFP: "We saved between 500 and 600 people. I made a dozen trips with the lifeboat, it was cold and windy."
"We are the heroes -- the Colombians, the Hondurans, the Chinese, the crew made up of 20 nationalities," he said.
The people on board included some 60 nationalities, although nearly a third of the passengers were Italian, followed by Germans and French.
Even before the accident, some supersticious sailors regarded the Costa Concordia as cursed after the champagne bottle used for its christening ceremony failed to smash when it was thrown against the hull.
The disaster happened just hours after the ship had left the port of Civitavecchia near Rome at the start of a Mediterranean cruise -- and before passengers had had time to take part in the ship's emergency drill.
Genoa-based Costa Crociere is Europe's biggest cruise operator, with a turnover of 2.9 billion euros ($3.7 billion) in 2010.