The BOA took Wada to the Court of Arbitration for Sport in a bid to keep the ban but were defeated yesterday.
Wada director-general David Howman said: "At the end of the day they have wasted a lot of time and a lot of money and got the inevitable result."
Howman said the BOA had a deadline of May 18 to change their bylaw or face being reported to the International Olympic Committee for remaining "non-compliant" with the world anti-doping code.
He had earlier claimed in a New Zealand radio interview that the BOA "had been held up to ridicule."
And he added: "The issue for the BOA is the rest of the world is looking at you and saying: 'What have you done this for?'"
BOA chairman Lord Moynihan "has expressed views which have hardly had any touch with the real facts and the real situation in relation to anti-doping."
The BOA are pushing Wada to change the code to make it a minimum four-year ban for a first serious offence.
Howman warned that that could cause legal problems.