Neymar (centre) scored both goals as Brazil eased to victory against Scotland
A banana was thrown onto the field during Brazil's 2-0 victory and Neymar accused some fans of racist behaviour.
But the SFA said: "The Scotland supporters are known the world over for their impeccable behaviour."
And police match commander Mark Sheeran said: "The Scottish fans' behaviour was first class. There were no issues at all inside the stadium."
The SFA also say they will contact the Brazilian Football Federation and the match organisers, Kentaro, to inform them of their information and of supporters' widespread unhappiness at the accusations.
A statement added: "The Scottish FA also refutes claims from Neymar that he was the victim of racist jeers. There was no evidence of such instances but the Scotland supporters have confirmed they booed the player for perceived unsporting behaviour during the match.
"The tens of thousands of Scotland fans who travelled to London were, in fact, commended for creating a carnival atmosphere not just inside the stadium but across the city throughout the weekend."
Brazil midfielder Lucas Leiva removed the banana from the penalty box Scotland were defending in the 83rd minute of the friendly match at Arsenal's Emirates Stadium.
And the majority of fans behind Allan McGregor's goal at that time were Brazilian.
Asked to comment on the banana incident, Liverpool midfielder Lucas said: "There is no more space for racism in the world.
"They say it's the first world here in Europe, but it's where it happens the most. That has to change.
"Everybody is equal today. It's a matter of respect."
Teenager striker Neymar, who scored both goals, was jeered by some spectators after receiving treatment in the first half following a Scott Brown challenge.
And former Scotland international Pat Nevin explained that the booing was a result of the Brazilian's playacting.
"He's one of those guys who lives in an alternative universe where the slightest brush leads to mortal pain as if it's going to kill him and then 20 seconds later it's magically got better," said Nevin, who was summarising the match for BBC Radio 5 live.
"I was getting infuriated really early on in the game with his actions when he was doing that because he's so brilliant, and that was what I thought the Scotland fans were shouting at.
"They were furious with all the diving about, rolling about feigning injury. If there was any racist abuse in the midst of that then I would be quite surprised but also completely and utterly disgusted and horrified because that doesn't sound like the Tartan Army."
Neymar, a reported target for many leading European clubs, made it three goals in three games for Brazil in a very one-sided affair.
But a memorable day for the 19-year-old was soured by the incident involving the banana and the catcalls.They were jeering me a lot, even when I was about to kick the penalty
"This atmosphere of racism is totally sad," Neymar told a Brazilian TV station. "We leave our country to play here and something like this happens."
"They were jeering me a lot, even when I was about to kick the penalty the entire stadium was jeering.
"It's sad. I would rather not even talk about it, to keep the subject from escalating."
Brazil head coach Mano Menezes admitted he hadn't seen the incident, while Scotland manager Craig Levein added: "I don't know anything about that."
Meanwhile, Menezes believes Neymar, who has been linked with Real Madrid and Chelsea, would improve if he moved to England but would be a loss to the fans in Brazil.
"I think that could only be good for Neymar as it would be a confirmation of his development," he said.
"English football would make him stronger and help to escape strong marking.
"I don't see any problem.
"But Brazil fans will be deprived of watching a good player."
Menezes was diplomatic when asked if any of the Scottish players had impressed him.
"Scotland does not depend on individuals, it is a collective work," he responded.
"They had players missing like Darren Fletcher, who is important for Scotland and Manchester United, so they certainly have good individual players some of whom play in England.
"But Brazil controlled the game well so we could not see anything of their individual players."