Vettel was punished after making a mistake in Sunday's race in Montreal while under pressure from Mercedes' championship leader Lewis Hamilton, who finished second but was declared winner.
Brawn recognised that the five second penalty added to Vettel's time after the race had triggered a lot of debate.
"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," he said in a review of the weekend.
"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," added the Briton.
"That's why transparency is important when it comes to explaining the decisions of the stewards, especially in such a complex sport as Formula One."
Brawn, a title-winning former Ferrari technical director and ex-Mercedes team principal, suggested working with the governing FIA to find a way for stewards to explain their decisions to the fans and how they reached them.
Five stewards review and decide on incidents during races, reviewing an array of data and video evidence in a very tight time frame.
They are also aiming to be consistent with previous decisions.
While Sunday's penalty triggered an outcry that the officials had wrecked a thrilling battle between Vettel and Hamilton, it was recognised by others that they had applied the letter of the law.
Whether the rules are fit for purpose, and how much discretion the stewards should have exercised, was another debate.
Brawn said he would not comment on the decision, given his position and Ferrari's stated intention to appeal, but fans could be assured that it had been taken impartially.
"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," he said.
Mercedes have won the first seven rounds of the season and are running away with both championships while Ferrari have not won since the U.S. Grand Prix in October last year -- a 10-race drought.
Brawn hailed Vettel as the "star of the weekend" and could understand the four times champion's disappointment and frustration.
(Reporting by Alan Baldwin; Editing by Hugh Lawson)
