Brailsford has said "mistakes were made" by Team Sky relating to anti-doping and medical procedures, but that "there is a fundamental difference between process failures and wrongdoing".
The team remains embroiled in controversy relating to a 'mystery' package which was delivered to then Team Sky doctor Richard Freeman at the 2011 Criterium du Dauphine, a race won by Sir Bradley Wiggins, and three therapeutic use exemptions (TUEs) granted to Wiggins in 2011, 2012 and 2013.
On Tuesday, Team Sky published a letter (PDF) and supporting documents sent by Brailsford to Damian Collins MP, chairman of the Culture, Media and Sport select committee, in which Brailsford reiterated his belief that the team was not guilty of breaching anti-doping rules.
Moments after the statement was published Graham McWilliam, the chairman of the Team Sky board, used Twitter to say the board remained "100 per cent behind the team and Sir Dave Brailsford" following suggestions that some riders might want the team principal to resign.
Brailsford has said he was told the package contained the legal decongestant Fluimucil, but as yet no documentary evidence has been produced.
"Self-evidently, the events of recent months have highlighted areas where mistakes were made by Team Sky," Brailsford wrote.
"Some members of staff did not comply fully with the policies and procedures that existed at that time.
"Regrettably, those mistakes mean that we have not been able to provide the complete set of records that we should have around the specific race relevant to UKAD's investigation. We accept full responsibility for this.
"However, many of the subsequent assumptions and assertions about the way Team Sky operates have been inaccurate or extended to implications that are simply untrue.
"There is a fundamental difference between process failures and wrongdoing. Our commitment to anti-doping has been a core principle of Team Sky since its inception. Our mission is to race and win clean, and we have done so for eight years."