He claimed Sky had only been abused by fans in France, and not those at the Giro d'Italia, which Froome won last May.
Sky then picked Bernal for its eight-man team to help Froome shoot for a fifth Tour title.
Britain's Geraint Thomas, fresh from winning two stages in the Alps, remained in the leader's yellow jersey. By the start of the 2018 Tour, he had earned an impressive collection of 59.
Four-time champion Froome can pull level with the likes of former five-time winners Jacques Anquetil, Bernard Hinault, Eddy Merckx and Miguel Indurain if he triumphs on the Champs Elysees next Sunday.
Lappartient added: "I can understand he (Brailsford) is annoyed the public are not passionate about his team and that they've been whistled".
After 14 stages, the 33-year-old is placed second on general classification [GC], only one minute 39 seconds behind the best rider in the race.
Spanish rider Gorka Izaguirre finished second, 15 seconds behind, and Yates crossed third with the same time.
Despite three tough days in the mountains up ahead, only one of them - stage 17 - ends on a mountaintop.
With 99 seconds in hand, this is Thomas' Tour to lose.
Froome was initially barred from starting his title defence by organisers because of the suspicion surrounding his "adverse analytical finding" for the asthma drug salbutamol at the Tour of Spain a year ago. He would be allowed to start but his presence in the peloton has been received with considerable scorn from the public.
It was in the same descent that Italian Fabio Casartelli crashed and died in the 1995 Tour de France. Froome has said his training plan was designed for him to come good in the last week. "It was my first professional race and it was awful".
Jeff Pachoud AFP Getty Images
But what happens when two team-mates are competing for the lead? On the following stage to Alpe d'Huez, his ambitions went completely up in smoke. He is, it would seem, also much more popular than the defending Tour champion.
"It was a very annoying climb of Alpe d'Huez". And that's when the statements began to change a little.
"We're good mates, we've ridden in same team for 10 years now, we've generally lived in the same areas as well, and trained together", said Thomas. "Then you have a team in the front". "We'll review the stage after today and see where we're at..."
"We just get on". "It's fantastic. It was a flat stage and everyone in the group recovered and I think everyone is happy it was a relaxed stage".
Brailsford, who has previously been questioned by a British parliamentary inquiry following allegations Sky had breached ethical guidelines by abusing the legal use of Therapeutic Use Exemptions (TUEs) for their riders, hit out at treatment of his team on Monday.
Adding spice is the fact the organisers, with a nod to Formula One, will line up the top 20 riders on a grid, according to their overall times.
The Tour is no ordinary sporting event and Team Sky is no ordinary team.
Froome was more evasive when asked if he would attack Thomas if in a position to do so.
Team Sky have become accustomed to a hostile reception in France as their domination of the race has grown since Bradley Wiggins's victory in 2012, as a combination of weariness with their success and suspicion over their practices have whipped up animosity among spectators.
"I'm not sure they would like to have seen their football players being spat at [the FIFA World Cup] in Russia", Brailsford said.
The Atlantic: Against the US, Putin's Russian Federation has an advantage - weakness
"For whatever reason, this president acts like he's compromised ", Schiff told ABC's This Week. I guess his supporters say he may have done that behind the scenes.