He said Carnival prides itself on providing people with a great vacation "and clearly we failed in this particular case."
He also said he plans to go aboard the ship and personally apologise to passengers.
Miserable passengers told stories of overflowing toilets, food shortages, foul odors and dangerously dark passageways.
As the ship docked, anxious passengers were lining the decks waving, cheering loudly and whistling to those on shore.