Shane Sutton resigned as the body's technical director on Wednesday amid claims of discrimination against elite cyclists, which the Australian denies.
Brailsford, Sutton's predecessor, has promised to co-operate with an inquiry into bullying claims.
"The British Cycling model wasn't based around motivation through fear or performance through fear," he said.
Brailsford, speaking to BBC Radio 4's Today programme, added: "You can't get performance on a continuous basis over a long period of time through fear. I just don't believe it."
Sutton, 58, was made British Cycling technical director in 2014 when Brailsford stepped down after a decade in charge, but is alleged to have used derogatory words like "wobblies" and "gimps" to describe Para-cyclists.
Former European sprint champion Jess Varnish also claimed Sutton made sexist comments towards her and told her to "go and have a baby".
Sutton has said he "rejects the specific claims".
Brailsford has promised to share his knowledge of the workings of British Cycling with an independent review into claims of bullying and discrimination, to be led by Annamarie Phelps, the chair of British Rowing.
"It's really good that this inquiry has been brought in, so we can establish the truth," Brailsford said.
"I'm not going to go into the details. What I will do is I'll share everything that I know with that inquiry."
Great Britain won eight gold medals at the Beijing Olympics in 2008 and matched that total four years later at London 2012, when Sutton was head coach and Brailsford was performance director.
Sir Dave Brailsford has dismissed the idea that British Cycling tried to motivate its riders through fear.