Nacer Chadli's 94th-minute strike secured a sensational victory for the Red Devils in Rostov-on-Don, as Martinez's side came from two goals down to win 3-2.
All five goals came in a frantic second half - Japan racing ahead before Jan Vertonghen's header sparked the turnaround.
And Martinez said his side thrived once the pressure was off at 2-0 down, adding that it puts Belgium in good stead for their clash with Brazil on Friday.
"When you play Brazil, you have to understand they are the best side in the competition," Martinez told a news conference.
"The quicker you understand your role, everything gets clear. Against Brazil, we will have clarity of how to play against the quality of individuals like [Philippe] Coutinho or Neymar who can decide the game in one second.
"But I think we need to learn from today, we played our first half with a fear of being favourites.
"When we went 2-0 down, we had nothing to lose, and we could enjoy the opportunity of getting back into it.
"Against Brazil, we can enjoy from the first minute. I don't think we are favourites. I don't think everyone expects us to go through to the semi-finals.
"It is a game when you're little you dream of being in a World Cup facing Brazil in a quarter-final, so we can enjoy it from the first second."
93:43 – Nacer Chadli has scored the second latest goal within the 90 reglamentary minutes of a knockout round match in World Cup; only Francesco Totti scored a later goal (94:24), which was against Australia in 2006. Timing. pic.twitter.com/lIULDUtl6L— OptaJavier (@OptaJavier) July 2, 2018
Japan were more than worthy of the lead given to them by Genki Haraguchi after the interval, and Takashi Inui's strike four minutes later put Belgium on the brink.
Eden Hazard had struck the post, but Belgium relied on good fortune when Vertonghen's looping header found the net, setting the stage for substitutes Marouane Fellaini and Chadli to complete the comeback.
However, Martinez - who acknowledged Belgium's slice of luck - refused to discuss his side's tactics, instead focusing on the attitude of his players.
"Today is not a time to speak about systems," the former Everton boss added. "We had over 20 opportunities at goal.
"The reality is we went 2-0 down and then you have to find solutions, reaction but what you have to find more than anything is the desire of the players that are desperate to perform.
"The same way that Hazard hitting the post is an unlucky move, Vertonghen's header is lucky.
"You need that luck to get that first goal, but overall, creating over 20 chances, it shows the hungry nature of this group. Today is not about tactics, mistakes, it's about the desire of players who wanted to get into the quarter-finals and face Brazil."
Belgium will square off against Brazil on July 6 at the Kazan Arena.