BA said 400 staff members had volunteered to come in on their day off to sort through the mountain of 15,000 lost items of baggage.
Mr Walsh said computer problems had arisen which had not occurred when the system was tested. But he admitted that the airline's performance had " not been good enough".
A total of 37 flights – mostly short-haul flights to other UK airports or European destinations – were cancelled yesterday and his press office said it "could not promise" there would not be more cancellations this week.
While many customers said they had had no problems, others complained they only learnt of cancelled flights on their arrival. In a statement, Mr Walsh said: "We are sorry for the disruption and inconvenience caused to customers whose flights have been cancelled or whose bags have been delayed.
"We will not rest until our service has been restored to the high standard customers rightly expect. A backlog of undelivered bags has built up. This backlog is not affecting the day-to-day operation of the baggage system, and we are making every effort to reunite delayed bags with their owners."
However, it could be some days before the bags are reunited with their owners because "left luggage" has to be subjected to extra security checks.
Kerry Johnstone, 35, said she arrived to discover that her scheduled flight to Copenhagen was cancelled. She said: "It is appalling that such a big organisation has got it so wrong."
Ministers who are backing the expansion of Heathrow with a third runway, also face a backlash over the problems caused by the opening of T5.
David Davis, the shadow home secretary, said: "It is a dreadful national embarrassment...it seems to be the way with some of these big infrastructure problems. This was being held up as a great piece of design and a great piece of organisation. It is astonishing frankly that this was allowed to happen."
Ruth Kelly, the Transport Secretary, said: "I have spoken with BA and the British Airports Authority and while the problems at Terminal 5 are for them to resolve I have made clear that the Government stands ready to assist where appropriate.
"Everything possible must be done to deliver a better service for passengers who are unfortunately still facing disruption and delays to their journeys."