He also called the past year a "malicious witch hunt" and a "living hell for me and my family".
UKAD announced on Wednesday that it would not press any charges after concluding an investigation into a "mystery" medical package delivered to Wiggins during the 2011 Criterium du Dauphine, when he raced for Team Sky.
Nevertheless, Wiggins also wrote: "Had the infrastructure for precise record-keeping been in place, this investigation would have never started".
Wiggins reserved his strongest criticism for Ukad and demanded the anti-doping body reveal the source behind leaked information which sparked the expensive 14-month investigation, claiming it is now in the public interest to release full details of the process.
Brailsford, who has since left British Cycling, told MPs previous year that the package contained the permitted decongestant Fluimucil and not, as has been alleged, the corticosteroid triamcinolone.
U.K. Anti-Doping was investigating whether the product was in fact a banned corticosteroid.
Wiggins, Sky and British Cycling were all told they would not face any charges for wrongdoing after UKAD said they had been hampered by a lack of "contemporaneous evidence".
UKAD chief executive Nicole Sapstead said a lack of accurate records had caused problems. This is a serious concern.
Wiggins ended the statement by saying that he was assessing "which legal options to pursue" and asked the media to give him and his family some space.
"At times it has felt like nothing less than a malicious witch hunt", added the five-time Olympic gold medallist.
"To say I am disappointed by some of the comments made by UKAD this morning is an understatement", he added. "No evidence exists to prove a case against me and in all other circumstances this would be an unqualified finding of innocence". However we accept that the relationship between British Cycling and Team Sky developed rapidly and as a result, at times, resulted in the blurring of the boundaries between the two. Team Sky's Chris Froome, his former teammate, has won it four times since.
"British Cycling have implemented a number of significant changes to the management of our medical services to the Great Britain Cycling Team following a review instigated in March by chair Jonathan Browning, shortly after his appointment".
As part of their investigation, UKAD interviewed 37 members of Team Sky and British Cycling, including medical professionals and riders from both organisations.
"We are pleased that UK Anti-Doping have concluded their investigation and that they will not be taking any further action", the team said in a statement.