Last October, Sky severed ties with Belgian Geert Leinders, a former doctor at Rabobank who is under investigation by the Belgian judicial authorities after being implicated by former riders. Leinders has denied any involvement in doping.
"The whole thing is my responsibility. I will take that squarely on the chin. It's something I regret, it's a mistake," Brailsford told a news conference.
"I should not have done it. I made an error of judgment."
Team Sky have been under the microscope since last year when they started to dominate the field in ruthless fashion, with 2012 Tour de France champion Bradley Wiggins repeatedly being grilled on doping.
Things have been no different for Sky's current Tour leader Chris Froome, who said on Saturday after claiming the yellow jersey that he is "100 percent" clean.
He had to repeat it on Monday, the first rest day in the three-week race.
"I know that what I'm doing is right, I know that the stage I won two days ago ... I know that result will never be stripped," said Froome, who finished last year's Tour as runner-up to Wiggins.
There will be more questions to come along the road to Paris.
"At the end of the day we all know the level of suspicion that is in or around the sport and it's only right that we have to sit here and answer questions," Brailsford said.
"We have to take it on the chin, that's the reality."
This year's Tour is the 100th but it is also the first one since American Lance Armstrong lost the seven titles he won from 1999 to 2005 before admitting to cheating his way to glory.
- Sports & Recreation
- Bradley Wiggins
- Chris Froome