Les Bleus overcame their European neighbours in Tuesday night's World Cup semi-final in St Petersburg to condemn Belgium's stellar squad to the third-place playoff on Saturday.
"It was a dead ball situation which was the difference," Martinez told BBC Sport after the game.
"It was a close game and it was very tight and it was going to be decided by that bit of luck in front of goal. The attitude of the players was brilliant and we couldn't ask for anymore. We have to understand one team wins and the other loses, and we did what we could.
"[The France goal] is the type of detail that counts in the semi-final of the World Cup. We have one game left and I want to ensure we finish the tournament on a high because these players don't deserve to leave here with a bad taste."
The second semi-final takes place in Moscow on Wednesday, with England locking horns against Croatia.