Captain Francesco Schettino appears to have ignored the firm’s emergency procedures “which are in line with international standards”, Costa Crociere said in a statement.
Francesco Schettino is suspected of manslaughter, but denies wrongdoing.
At least five people have died but about 15 remain unaccounted for. Divers are trying to find more survivors.
“It seems that the commander made errors of judgement that had serious consequences,” the statement by Costa Crociere said.
The Costa Concordia is lying on its side just off the Tuscan island of Giglio, where it ran aground.
But Captain Francesco Schettino has said that the rock it hit was not marked on his nautical chart.
“We should have had deep water beneath us… We were about 300 metres (1,000ft) from the rocks more or less. We shouldn’t have hit anything.”
He also denied claims by prosecutors that he left the Costa Concordia before evacuation was complete.
“We were the last to leave the ship,” Francesco Schettino told Italian TV.
Captain Francesco Schettino, 52, has worked for Costa Cruises for 11 years. First officer Ciro Ambrosio has also been detained.
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