Lewis Hamilton, just one of four drivers who had spectacular rear failures during the Silverstone race, was comfortably leading when he had his problem.
Afterwards, the furious Briton told reporters he was trying to hold his tongue.
"Big time," he relented when asked if he is worried about safety.
"They need to do something," Hamilton told British broadcaster Sky.
On the BBC, the 28-year-old could hold his tongue no longer.
"It's unacceptable," said the Mercedes driver, whose teammate Nico Rosberg – who won – also had a partial tire failure just as a safety car period began.
On-board footage from Kimi Raikkonen and Fernando Alonso's cars showed how the big chunks of flying tire debris could have hurt a driver.
"It's only when someone gets hurt that someone will be doing something about it," Hamilton charged.
"I think it's a waste of time talking to the FIA, and if they don't do anything that says a lot about them."
McLaren managing director Jonathan Neale, whose driver Sergio Perez had one of the exploding failures, insisted: "We have to make sure our drivers are safe."
Jenson Button agreed: "The cars behind get hit by rubber that has metal in it. It's obvious it's got to change. It's very scary."
Recently, Pirelli wanted to make a fundamental change to the tire construction – replacing an internal steel band with a kevlar one – to stop delaminations, but teams like Lotus blocked the move.
F1's official supplier instead had to tackle the issue by deploying a new kind of glue to bind the tread.
All the talk immediately after the race on Sunday was about the obvious need for Pirelli to change the tire construction, whether or not the teams agree.
Pirelli's Paul Hembery refused to immediately comment pending an investigation, despite the international media relentlessly bombarding him with questions.
"Sorry," he told them. "When we have the answers, we'll let you know."
Meanwhile, a gearbox failure for Sebastian Vettel means the Red Bull driver's points lead over Fernando Alonso was slashed from 36 to just 21 points.
Ferrari's Alonso, however, was not celebrating.
"We know we have a lot of work to do," said the Spaniard, who has complained all weekend about the lagging development of his car.