The Spaniard went on to urge his players to raise their game in their upcoming semi-final clash with France, who defeated Uruguay in the day's other quarter-final.
"They did it. You saw incredible heart from this team," BBC Sport quotes Martinez as saying.
"You have to accept that Brazil have finesse and they will break you down but we did not accept it. This is something special. These boys deserve to be real special people back in Belgium.
"I never lost a game on the tactics board, it's the execution that matters and the execution was magnificent. Players have to be brave to change the way we play and we had two days to do it. That is down to desire, they wanted to make it happen.
"It is special. We can't let them down back home now. We have beaten Brazil in the World Cup, we have created a nice memory, let's treasure it and pass it down. Now we need more energy for the semi-final."