Despite fighting to a 2-1 win on the night, to level the tie at 2-2 on aggregate, Downs were eliminated from the competition due the away-goals rule, and will now contest the second tier CAF Confederation Cup group stage.
During the match, villainous tactics from the visiting side were obvious as the goalkeeper Nelson Lukong feigned injury on numerous occasions in an attempt to delay the restart of play, particularly from goal-kicks.
This visibly aggravated the Brazilians' supporters as they eventually broke through the fence, shortly after the referee blew the final whistle, and the players and officials were called to calm them down by joining in their traditional singing and dancing.
However, Mosimane says South Africans need to adopt the trade of the "win at all costs" mentality which teams from across the continent have if they are to succeed in matches of such competitive nature.
"I think it's good for you journalists [to talk about delaying tactics]. Remember I was one time in Bafana and Itumeleng Khune was delaying and doing the tactics - you guys hit him hard," said the former Bafana Bafana coach.
"And the notes that I passed around - what notes? Did you see what they [AS Vita] did? Do you think the linesman doesn't see?
"Once the referee goes and turns his back, the goalkeeper falls and the centre-back is supposed to take the goal-kick but he's not kicking it; he gives it to the other one...
"The goalkeeper fell how many times? And then how many minutes added? Four."
'Jingles' reiterated that they are going through a learning phase and says people must understand that 'fair play' is only a myth when it comes to continental football.
"So we'll come and we'll pay our school fees. South Africa is learning; I hope everybody is watching and seeing that it's a win at all cost," he added.
"It has nothing to do with fair play; which fair play? Did you see how they celebrate? They don't care. They won, finished. We can cry and lament and whine, okay, they'll give us tissue papers."