British Cycling and Team Sky have been under scrutiny over the package delivered to the 2011 Criterium du Dauphine in which Bradley Wiggins was riding.
Wiggins' then coach Shane Sutton, giving evidence to a Parliamentary inquiry into doping in sport, earlier said he did not know what the package contained. The chair of British Cycling's Ethics Commission George Gilbert said it could have been pedals.
Brailsford shed more light on the situation, however, after he said he had been given permission to do so by United Kingdom Anti-Doping which is investigating allegations of wrongdoing in the sport.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
He said Team Sky doctor Richard Freeman had told him it was Fluimucil - a product to treat coughs and sore throats.
"Doctor Freeman told me that it was Fluimucil that was in the package, a product that is for a nebuliser. That is what was in the package," Brailsford told MPs.
Brailsford repeated Sutton's comment that British Cycling coach Simon Cope had brought the package with him on a pre-planned logistical trip.
Admitting he was "pained" by the shadow cast over British Cycling by the investigation, Brailsford said the package had only recently been brought to his attention.
"Let's just be clear, I wasn't aware of the package at the time. When it was brought to my attention, it is my role to take those matters seriously to try and gather the facts and see if there was any need for a disciplinary procedure," he said.
"My first course of action was to speak to all of the guys on the team. I got witness statements, and then I couldn't see that there was any anti-doping rule violation.
"However, I also felt that it was probably appropriate to pass that on and have it viewed by an independent authority who could verify the fact."
Asked why Team Sky had flown out the Fluimucil, a permitted drug on the WADA list, rather than buy it locally, Brailsford acknowledged that it did seem "extreme" but said it was normal to get supplies from their own stock in Britain.
Brailsford said Team Sky regularly gave Fluimucil to their riders to treat colds.
"As a cycling team we are constantly moving around late at night. (Simon) was on his way anyway and brought it down with him. He has his own stores in Manchester so brought it with him. That was the decision made and I totally understand it."
Sutton had earlier said it was not his job to know what medication 2012 Tour de France winner Wiggins was taking.
"Never even thought to ask," Sutton said. "I know Brad was suffering towards the end of the Dauphine."
(Reporting by Martyn Herman, editing by Ed Osmond)
