The pair were among four drivers to have dramatic tyre blow-outs during the Silverstone race, with Hamilton's coming while his Mercedes was leading on lap seven.
Several other drivers reported tyre troubles during the event.
"The safety is the biggest issue," said Hamilton. "It's just unacceptable.
"We had that tyre test to develop and improve the tyres to stop that from happening and after that tyre test they didn't do anything.
"Someone could've crashed. I was thinking behind the safety car that it's only when someone gets hurt that something will be done about it."
McLaren driver Perez echoed Hamilton's forthright comments.
"This is unacceptable, we are risking our lives and we shouldn't wait until something happens to all of us," he said.
"If it happens at 250km/h it will be a big shame so Pirelli has some work to do."
When asked if he would talk to Pirelli or the FIA about the events of Silverstone, Hamilton said any such conversations would be pointless.
"I think it's a waste of time talking to any of them at the moment," he said.
"They can see what happened today. They have to react to it."