Immediately after the race in Brazil, Hamilton took the blame for the contact between himself and Red Bull's Alexander Albon, which denied the rookie his maiden podium in Formula 1.
Vettel and Leclerc were also involved in a collision with each other, which eliminated both from the race with just a handful of laps to go.
A stewards investigation saw the stewards take no further action on the incident, with team principal Mattia Binotto calling the clash a "silly action".
Brawn believes that both Ferrari drivers can learn from Hamilton and step up to take responsibly for the incident.
"I wouldn’t want to venture an opinion on who was most at fault for the collision, but in the cold light of day, maybe it would be good if one of them will follow Hamilton’s example and immediately admit culpability, as the champion did regarding his clash with Albon,” said Brawn, in his post-race debrief.
“If Ferrari really wants to put an end to Mercedes’ dominance, not only does it need to provide its drivers with a more competitive car next year, it must also ensure that incidents like this one are not repeated. Formula 1 is a team sport, especially so in Maranello.”
In order to calm tensions within the team, the responsibility falls onto the shoulders of Binotto, according to Brawn.
“After tensions flared in the races following the summer break, everything seemed to have calmed down in the Ferrari dressing room.
"But now, Mattia Binotto faces the tough task of getting things back on track and indeed he said just that in his interviews after the race.
“He had to get stuck in and tell the drivers to face up to their responsibilities, which in Maranello always means putting the interests of the team ahead of those of the individual, which was not the case in Sunday’s race.”
Bahrain International Circuit - Winter testing