The British manager suggested the first Tour de France after the Lance Armstrong affair was "probably the worst Tour to try to win."
Speaking to a group of media, including the Cyclingnews video team, Brailsford said sentiment and suspicion was understandable but called on people to back Froome.
"You'd expect that the public who trusted in this sport for a long time to be a bit angry and a bit frustrated with what they found out. It's understandable," Brailsford said.
"I think people believed in the Lance era when deep down maybe they knew they shouldn't have. They are [doing that now] and disbelieving in Chris, where deep down they probably know they should."
"Where the authorities look back on the Armstrong era and think 'we did a bit too little at that time to uncover what was going on', I'd say that hopefully they say now that they're doing a bit too little to protect Chris and demonstrate the support he deserves, that's my take on the situation."
Brailsford said he feels hurt for the doubts about Froome.
"We can't expect people to have 100 per cent confidence in this sport after the recent past, but I think we can optimize the level of confidence and get it as high as it could realistically go," he said.
"We'll do everything we can to achieve that because Chris and the rest of the team have work incredibly hard for this. He's been fantastic member of team for a number of years. He started from very, very humble beginnings in bike racing and made himself to top of podium. He's doing it the right way. And while we've got to be patient, when I watch, I know what's going on, and I watch someone is absolutely doing it the right way, the same as the whole team. And when you watch the treatment that he gets, it's quite hurtful, you feel for the lad and I don’t think he deserves it."
Brailsford appeared irritated by suggestions from the media that the Grappe power analysis was not complete and that more should be done to help prove Froome performances are credible.
"I think we've got to be careful. Because every time we try and support something if all you guys are going to do is say 'It's all well and good but you haven't don’t that,' we're not going to win are we? Either we get behind this lad or we don't," he said.