Walsh told members of Parliament's Commons Transport Committee "I take responsibility for the issues that went wrong," with the March 14 opening of Heathrow Airport's Terminal 5, The Daily Mail reported Thursday.
Flight delays and baggage mishaps plagued the $8.41 billion terminal's first weeks.
Walsh said mistakes were made partly because the administration reduced testing of the new facility to make up for construction delays.
"We let our customers down. We could have done better and should have done better," Walsh said.
Two airport executives have resigned in the wake of the terminal's disappointing opening.
Walsh said he wouldn't resign but said his job tenure was "a matter for the board" to decide, The Daily Mail report said.