The 21-year-old was unable to set a final lap after he failed to cross the line in sufficient time.
As he prepared for his last shot at improving his grid position, the Dutchman was passed by Sebastian Vettel, Daniel Ricciardo and Nico Hulkenberg.
After being urged to speed up by his race engineer Gianpiero Lambiase, Verstappen yelled: "They are such w******, honestly.
"You're trying to be nice but everybody's just f****** it up."
F1 Chinese Grand Prix in pictures
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Verstappen will start fifth, behind both Mercedes and Ferrari cars. Valtteri Bottas lines up on pole for the first time since the Russian Grand Prix last October.
Later, speaking to Dutch TV, Verstappen claimed drivers should not overtake one another as they gear up for their speedy laps. He also vowed to gain revenge the next time he qualifies for a race.
"We were just staying neatly behind each other, but at a certain point Vettel passed me and the two Renaults as well," said Verstappen.
"So they f***** up my entire build up. There is an unwritten rule that you just follow each other. From now on in qualifying, I'm going to f*** them up as well."
Verstappen was sentenced to two days of public service by Formula One's governing body after he shoved Esteban Ocon three times following the conclusion of last November's race in Brazil.
The Red Bull driver, furious that the Frenchman had cost him victory following their crash, was also warned about his future conduct by the FIA.
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