Brawn, F1's managing director, also likened the decision-making process - and the "transparency" that is required - to the use of VAR in football.
Vettel's five-second penalty for forcing Lewis Hamilton off the track cost him a race victory in Montreal and sparked major controversy and debate, with many unhappy that it spoiled a great battle between two multiple world champions.
Vettel even claimed himself that he wished he drove in a different era, such is his dissatisfaction with certain aspects of modern F1 and its rules.
"I can understand how Vettel feels and I know Ferrari intends to appeal the decision," Brawn, formerly team boss at Ferrari and Mercedes, said.
"I also know what a difficult job the stewards have, as they have to reach a their decision in a very short time, producing a verdict that can affect the outcome of the race.
"I have a lot of respect for the work of the stewards and for their professionalism and I believe they would be the first to say that they would prefer not to see a race outcome decided via a penalty.
"At the same time, I understand how difficult it must be for fans to understand why the driver on the top step of the podium is not the one who crossed the finish line first."
Brawn accepted that F1 perhaps needs to take different views into account when making decisions, adding: "That's why transparency is important when it comes to explaining the decisions of the Stewards, especially in such a complex sport as Formula 1.
"It is in football, where despite the arrival of VAR, there is still discussion as to whether a handball should be punished with a penalty or not.
"Therefore, it might be useful to work with the FIA on solutions that would allow the stewards to explain their decisions to the fans and to elaborate on how they reached them."
Brawn continued: "Having said that, I would emphatically add is that there is nothing sinister about a decision like this.
"You might agree with it or not, but none of those who take on the role of steward each weekend has a hidden agenda and fans can be certain of that."
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