Back at Sauber, however, fellow Mexican Gutierrez is less panicked.
"The tyre (situation) is obviously more dramatic than last year," he is quoted by Spain's Marca newspaper, "but gradually the teams will adapt. It's a matter of finding the right fit.
"In testing we have already seen progress," the 21-year-old added.
Even Perez's teammate Jenson Button is not overly worried.
"This year is more difficult in terms of graining," he is quoted by Brazil's Totalrace, "but it's much easier now to understand the tyre.
"You put it in your window of operation and know that it will begin to grain from the third or fourth lap.
"Last year," Button continued, "there were teams who could make the tyre work, but they didn't know why. For the others it was a knife edge."
Pirelli's Paul Hembery, meanwhile, is adamant the cool weather in Barcelona - "freezing" last Friday according to Mark Webber - made the degradation of the 2013 tyres look much worse.
"We shouldn't see anything like it (the Barcelona weather) in the whole season," he is quoted by Spain's El Mundo Deportivo.
And some, like the famously phlegmatic Kimi Raikkonen, are not worried at all.
Asked to compare the 2012 Pirellis with this year's compounds, the Finn told Turun Sanomat newspaper in Russia on Saturday: "I don't see much difference."