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.

The 27-year-old former Aberdeen forward, who moved to Blackburn for £2m in 2011, has signed a one-year deal at League Two side Plymouth Argyle.
Goodwillie won the last of his three caps five years ago, scoring his only goal from the spot against Spain.
"I don't think about it too much, but as you get a bit older you think 'is it away from me?" Goodwillie said of his international hopes to BBC Radio Devon.
"If you're a player at any age, if you're performing well I don't see why you can't still think about it, but right now I'm just concentrating on club football."
Goodwillie scored just eight goals in two seasons at Aberdeen, and spent the final part of last season at Argyle boss Derek Adams' former club Ross County, for whom he scored once.
"It helps that he (Derek Adams) is Scottish and he knows about Scottish culture and he can put his arm around you," added Goodwillie.
"You're quite far from home and he'll understand that, and I think that was a big decision for me."
Goodwillie was on the scoresheet for Dundee United when they beat Adams' Ross County 3-0 in the 2010 Scottish Cup final.
"He's proven goalscorer, he's a player that has commanded a high transfer fee over a period of time," Adams told BBC Radio Devon.
"He's a very good football player. I think it's important that we take football players to this football club that enhance us on the pitch and he'll certainly do that."

The bird, which is named LM12, arrived on Thursday, the earliest reappearance of a resident bird there in almost 50 years.
Its mate LF15 is expected soon at the Scottish Wildlife Trust reserve near Dunkeld, which operates a live webcam of the nest.
The pair fledged three chicks in both 2015 and 2016.
Charlotte Fleming, Perthshire ranger for the Scottish Wildlife Trust said: "One of our eagle eyed volunteers spotted LM12 just after 17:00.
"He spent several hours in the nearby trees but didn't touch down on the nest until early this morning when he appeared carrying his breakfast.
"From the views we've had of his distinctive chest pattern and long wing tips we are as sure as we can be that it is LM12.
"He has also made himself well and truly at home, bringing in sticks and preparing the nest, which is further proof that he is the resident male."
Sir Dave Brailsford has dismissed the idea that British Cycling tried to motivate its riders through fear.
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David Goodwillie says he has not given up on representing Scotland once again.
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A male osprey has returned to its nest at the Loch of the Lowes reserve after its migration from West Africa.