The former British Cycling performance director, who has plotted four Tour de France triumphs for Team Sky, has come under fire for failing to prove what was in a medical package ordered by a team doctor at the 2011 Criterium du Dauphine.
"Of course I'm not hiding. I'm fine in myself and I've got confidence in my team," Brailsford said in an interview with magazine Cycling World at the Tirreno-Adriatico race.
"No (I'm not quitting). My thoughts are about what's good for the team and what's right. We're just here to win as many races as possible and do it the right way and that's my primary concern and that's what I think about."
Team Sky and British Cycling have both been subject of an investigation by UK Anti-Doping (UKAD) into allegations of wrongdoing in the sport. Both have denied any doping violations.
British lawmakers have also carried out an inquiry into a newspaper allegation suggesting the package ordered by Dr. Richard Freeman and administered to Bradley Wiggins was the powerful corticosteroid triamcinolone - the same product Wiggins took using a WADA-approved therapeutic use exemption (TUE) before winning the 2012 Tour.
Brailsford told lawmakers that the package contained the legal decongestant Fluimucil - although a lack of a paper trail has called in to questions Sky's medical record keeping.
The 53-year-old said he was "disappointed" that the start of the season had been overshadowed by the furore and said it should not reflect badly on his riders.
"This has nothing to do with them," Brailsford said. "On the other hand we've got to move forward. Personally, I'm fine."
Several Sky riders offered support for Brailsford on social media this week, although triple Tour winner Chris Froome was not one of them, leading to speculation that the relationship between the pair was under strain.
"We had a good conversation, that's it," Brailsford said.
Brailsford said he welcomed UKAD's investigation but insisted there had been no wrongdoing.
"On a personal level, I've been through a lot over the years and it's important to make sure that you can look at yourself and say that there has been no wrongdoing," he said.
"I'm confident of that."
Brailsford's highly successful time with British Cycling has also been scrutinised in a UK Sport investigation into the culture within the governing body's elite programme following the resignation of technical director Shane Sutton.
On Friday, British Cycling responded to a leaked draft of a report into the investigation published by the Daily Mail in which Brailsford was described as "untouchable".
"(The) World Class Programme leadership focused on medal delivery without sufficient care and attention to the overall staff and athlete culture and environment," it said.