Speaking after the game, and quoted by the BBC, Martinez was effusive in his praise for his side, saying: "They've done something special and I hope everyone in Belgium is very, very proud."
The 44-year-old also expressed his own pride in the Belgians' achievement. He explained: "I'm the proudest man on earth because I gave the players a very tough tactical assignment and the way they believed until the last second was incredible."
Martinez's tactics certainly paid off, not least his use of Axel Witsel and Marouane Fellaini as a defensive midfield duo. Brazil looked naive by comparison, as they were frequently exposed on the break - especially when Kevin de Bruyne scored the Red Devils' decisive second goal.
Martinez lauded the way in which his side responded to the challenges presented by the five-times World Cup winners, adding: "Brazil have so much finesse and you know that they can cut you open. But I didn't think for one second that the players would give up."
Belgium's victory on Friday enabled them to advance to the last four of the World Cup for the first time since 1986. They will face France in the semi-final in St Petersburg on Tuesday.
Martinez stressed the importance of focusing on the clash with Les Bleus, as he remarked: "Now we need more energy for our next game to try to make sure we're just as good in the semi-finals."
Ever since taking over as Belgium manager, Martinez has faced frequent criticism for his tactics and team selection. Now that the Red Devils have finally defeated a major footballing nation in a competitive match, his critics may need to revise their opinion of him.