Following the Lance Armstrong doping scandal, the British team asked riders and support staff to sign up to a written statement saying they had no past or present involvement with drugs.
Sports director Steven de Jongh and race coach Bobby Julich have since quit Team Sky, which won the Tour de France this year, after admitting to taking banned substances earlier in their careers.
"We started Team Sky with a very clear policy, we were going to try to recruit the riders and the staff who hadn't had previous convictions for doping and, to the best of our knowledge, had no previous involvement in doping," Brailsford told the Business in Sport & Leisure conference.
Brailsford said he had tried to look dispassionately at the issues raised by the Armstrong scandal. The American has been stripped of his seven Tour de France wins over allegations of systematic doping, plunging the sport into crisis.
"It was important to stick with the policy but we have to go through some pain, some short-term pain, some medium-(term) pain potentially and maybe even some performance pain to get to where we want to be," he told a business audience, setting out his strategy for handling the Armstrong fallout.
"We were willing to take a short-term hit on performance to get where we wanted to be for the long term."
Brailsford said those leaving the team were offered a "parachute payment" to help them and their families to cope until they could find another job and would be given good references for the work they had done for him.
The aim was to remove people who could otherwise pose an ongoing threat to the team if a past association with doping were to emerge, he added.
The Team Sky road race team was launched in 2010, an extension on the sponsorship agreement between pay TV company BSkyB and British cycling.
It set the goal of winning the Tour de France within five years and achieved its target in only its third season when Bradley Wiggins became the first Briton to win the race in July.