The 41-year-old Armstrong, who won the Tour de France seven times after surviving cancer, was accused of being part of the "the most sophisticated, professionalised and successful doping programme that sport has ever seen" by the United States Anti-Doping Agency.
USADA has banned Armstrong for life and stripped him of his Tour de France titles and on Wednesday it published the findings of an investigation into the Texan and his US Postal Service Pro Cycling Team.
Armstrong's lawyers described the allegations as a hatchet job, but Brailsford said the 1000-page report made it hard for anyone to trust cycling.
"It is understandable now for people to look at any results in cycling and question that," Brailsford told BBC radio.
"It completely and utterly lost its way and I think it lost its moral compass."
The comprehensive report contained the testimony of 11 of Armstrong's former team mates, that, according to USADA, provided undeniable proof Armstrong was at the centre of a sophisticated doping programme.
"It is shocking, it's jaw dropping and it is very unpleasant," Brailsford said.
"It's not very palatable and anybody who says it is would be lying wouldn't they?"
He added: "I think there are plenty of people out there who saw this guy and what he did as an amazing achievement.
"He is one of the first cyclists that maybe transcended the sport and became a hero beyond cycling.
"It was an amazing thing and people got behind that. So to now find out what was behind (it) is, of course, disappointing."
One of the team mates who testified against Armstrong was Michael Barry, who admitted to doping while he was a member of Armstrong's US Postal Service team and who rode under Brailsford for Team Sky from 2010.
"We signed Michael from HTC which was, at the time, highly regarded as being a very sound, clean team," Brailsford said.
"During his time at Team Sky, we have had absolutely no cause for concern whatsoever, there has never been any question in terms of his performances, his training, his behaviour on the team. There have never been any issues in that respect. But ultimately he lied.
"We set out with a zero tolerance policy, so we said that anyone who has had a doping conviction from the past or proved to have been involved in doping hasn't got a place on Team Sky. That is our policy.
"When you take someone you ask them a question and if someone lies to you and you find out later it's disappointing."
Britain's six-times Olympic champion Chris Hoy said the accusations were "pretty depressing".
"I haven't read the report but it's good to get it out in the open and show that nobody is too big," Hoy told Sky Sports.
"It's been coming for a number of years, trying to change the culture, and Team Sky's approach has been about zero tolerance so ambassadors like (2012 Tour de France champion) Bradley Wiggins can inspire people.
"The next generation can see that you don't have to take drugs to win the Tour de France.
"Every day in the Tour de France you have to field questions about are you on drugs. Bradley was frustrated but his frustration is not with the journalists or the media but with the previous generation who have let down the public.
"I'm a bit removed from it being a track cyclist but it's difficult having aspersions put on you but all you can do is win clean."
However, Team Sky's British rider Alex Dowsett told the BBC that Armstrong was "still a legend of the sport, a guy who had cancer, came back and won the Tour de France.
"I think it's not really important and I really don't think it matters," he said.