Belgium went into half-time 2-0 up thanks to a Fernandinho own goal and De Bruyne's fierce strike, giving a Brazil side previously seen as World Cup favourites a mountain to climb.
Brazil need to start thinking about Qatar 2022 after their World Cup exit at the hands of Belgium, according to 2002 victor Rivaldo.
But after a bright start from Tite's team, it was Belgium that looked the more risky, scoring through a Fernandinho own goal in the 13th minute and increasing its lead with a superb De Bruyne strike just after the half-hour.
Hazard on the ball.
"They weren't superior to us on the pitch, but more efficient".
"We feel bad because Belgium played well". Not for one minute were [Belgium] going to give up.
"Brazil adapted better in the second half", he added.
The World Cup favorites tripled Belgium's shot total (27 to 9), put nine shots on target and held 60 percent of the possession throughout the game.
Goalkeeper Thibaut Courtois made a number of fine saves and needed every inch of his nearly-two metre frame to deny Brazil's talisman Neymar with a glove in the dying minutes.
Five-time world champion Brazil came into Friday's quarterfinal match at Russian Federation 2018 as the clear favorite to beat the Red Devils and reach next week's semifinal versus France, which had dispatched Uruguay hours earlier.
Martinez also hailed his player for adapting to a new formation in such a short amount of time since their win over Japan.
De Bruyne, playing in a more advanced role than he had in Belgium's previous four matches, was at the heart of his team's best work, managing the transition from rearguard defence to attack with vision, pace and accuracy.
There is a steely determination about this Belgium side that they did not have four years ago when they narrowly lost a quarter-final to Argentina.
The Red Devils face Les Bleus, champions in 1998, on Tuesday in St Petersburg, bidding to reach the final for the first time.
Renato Augusto gave Brazil a lifeline in the 76th minute with a brilliant header but Neymar and Co could not find another goal to take the game into extra-time.
Brazil's forward Neymar controls the ball during the Russian Federation 2018 World Cup quarterfinal football match between Brazil and Belgium at the Kazan Arena in Kazan on Saturday.