The founder and chief executive of JetBlue Airways, his voice cracking at times, called himself “humiliated and mortified” by a huge breakdown in the airline’s operations that has dragged on for nearly a week, and promised that in the future JetBlue would pay penalties to customers if they were stranded on a plane for too long.

David G. Neeleman said in a telephone interview yesterday that his company’s management was not strong enough. And he said the current crisis, which has led to about 1,000 canceled flights in five days, was the result of a shoestring communications system that left pilots and flight attendants in the dark, and an undersize reservation system. Until now, JetBlue and its low fares have enjoyed overwhelming popularity and customer satisfaction ratings.

The crisis began Wednesday when an ice storm hit the Eastern United States. Most airlines responded by canceling more flights earlier, sending passengers home and resuming their schedules within a day or two. But JetBlue thought the weather would break and it would be able to fly, keeping its revenue flowing and its customers happy.

On the contrary, JetBlue’s woes dragged on day after day. On Saturday night, for instance, the airline said that the 23 percent of flights it had canceled on Saturday and Sunday would also be canceled Monday. The confusion led to angry exchanges between customers and employees, prompting the airline to call out security personnel.