The troubles struck the airport's new Terminal 5 building, which opened for business Thursday.
"There were problems in the car parks, airport areas, computer glitches, and the baggage system," said British Airways CEO Willie Walsh in a statement. "Our performance was not good enough. We did not deliver for our customers and we should have."
British Airways said it planned to operate 80% of scheduled flights, including all long-haul routes, from Terminal 5 on Friday, after canceling dozens of flights Thursday. The airline advised travelers to check arrival and departure information before leaving for the airport.
It also said customers whose bags were lost during the chaos could use the online tracing service at BA.com for real-time information.
One British newspaper called the situation at Heathrow's $8.5 billion Terminal 5, which opened amid great fanfare this week, "a national humiliation" that called into question the country's ability to handle the 2012 Olympics.
Much of the trouble stemmed from problems with the terminal's new computerized baggage-handling system. London's Daily Mail newspaper reported that baggage handlers were not able to log in to the system. As a result, British Airways said passengers could only board flights if they left checked luggage behind.
There also were reports that inadequate staff parking facilities caused many Terminal 5 workers to show up late at their positions, leading to more confusion.
The terminal has been hit with other problems, as well. On Wednesday, the U.K.'s Information Commissioner's Office ordered airport officials to suspend use of a biometric fingerprinting system due to privacy concerns.
Editor's Note: This story was revised March 28 to remove the names of tech vendors whose technology was not involved in the snafu at the airport.