Gerry Cahill said at a news conference Thursday night as the Triumph was docking in Mobile, Ala., that he appreciated the patience of the 3,000 passengers on board.
He says Carnival prides itself on providing people with a great vacation "and clearly we failed in this particular case."
He says he plans to go aboard the ship and personally apologize 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.
Copyright 2013 The Associated Press.