The Brit was among four competitors who suffered blowouts at Silverstone on Sunday.
Hamilton, who qualified in pole position, was leading the race before his left rear wheel burst during the eighth lap.
"The safety is the biggest issue, it's unacceptable," he told BBC Sport. "We had that tyre test to improve the tyre and to have four blowouts is unacceptable.
"It's only when someone gets hurt that someone will be doing something about it. 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."
The season continues next weekend with the German Grand Prix.