Ferrari driver Massa suffered one of the five blow-outs seen on track, with Mercedes' Lewis Hamilton and McLaren's Sergio Perez saying the situation was unacceptable.
With all incidents occurring at high-speed, Massa reckons the consequences could have been much worse.
"I think we were lucky that in all the accidents the driver was able to carry on without crashing," Massa said.
"But if that happens in a corner you can have a big accident and this is really not nice."
The Brazilian agreed with his rivals that the situation was unacceptable and that something needed to be done immediately.
"I think what happened today is unacceptable, because we are not talking about safety," he said. "What happened today was very dangerous for us, for me and for all drivers racing.
"It's not the same race that we've had this kind of problem. I had already had two tyre problems in Bahrain, and another problem here.
"Many other cars had problems before, so it's not the first track. Many people say it's because of the kerbs or the debris, but it's not the first time, so for me it's unacceptable and we need to do something for our safety."
Massa said he felt he had not been particularly aggressive when attacking the corners, despite suggestions that it could have been the kerbs causing the problems.
"No, I didn't hit the kerb very hard. The only debris I passed was the one from Lewis, because he was the first one to have this problem, but I don't remember being too aggressive over the kerbs."
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